From pas at www.economia.unimi.it  Tue Mar  1 18:29:22 2005
From: pas at www.economia.unimi.it (pas@www.economia.unimi.it)
Date: Tue Mar  1 18:29:40 2005
Subject: [Pas] Probability Abstract 85
Message-ID: <cd3fceed7eeaaedfbf0c01d58c85cdd6@unimi.it>


												March 1, 2005
												Letter 85

Dear Colleagues,

I am glad to inform you that the new probability mailing list PCML 
(Probability Community Mailing List) is now active. This list, as 
announced by Chris Burdzy in Pas83, will be moderated by David Aldous 
and Jim Pitman (Berkeley, USA). It is currently hosted on the same 
server of the PAS service in Milan, Italy.

Stefano M. Iacus

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---------------------------------------------------------------

3074. ASYMPTOTIC EXPANSIONS FOR INFINITE WEIGHTED CONVOLUTIONS OF HEAVY 
TAIL  DISTRIBUTIONS AND APPLICATIONS

Ph. Barbe and W.P. McCormick (CNRS and University of Georgia)

We establish some asymptotic expansions for infinite weighted 
convolution of
distributions having regular varying tails. Various applications to 
statistics
and probability are developed.


http://front.math.ucdavis.edu/math.PR/0412537

---------------------------------------------------------------

3075. STABILITY PROPERTIES OF CONSTRAINED JUMP-DIFFUSION PROCESSES

Rami Atar and  Amarjit Budhiraja

We consider a class of jump-diffusion processes, constrained to a 
polyhedral
cone $G\subset\R^n$, where the constraint vector field is constant on 
each face
of the boundary. The constraining mechanism corrects for ``attempts'' 
of the
process to jump outside the domain. Under Lipschitz continuity of the 
Skorohod
map \Gamma, it is known that there is a cone \mathcalC such that the 
image
\Gamma\phi of a deterministic linear trajectory \phi remains bounded if 
and
only if \dot\phi\in\mathcalC. Denoting the generator of a corresponding
unconstrained jump-diffusion by \cll, we show that a key condition for 
the
process to admit an invariant probability measure is that for x\in G, 
\cll
\id(x) belongs to a compact subset of \mathcalC^o.


http://front.math.ucdavis.edu/math.PR/0501014

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3076. SYNCHRONOUS COUPLINGS OF REFLECTED BROWNIAN MOTIONS IN SMOOTH 
DOMAINS

Krzysztof Burdzy and  Zhen-Qing Chen and Peter Jones

For every bounded planar domain $D$ with a smooth boundary, we define a
`Lyapunov exponent' $\Lambda(D)$ using a fairly explicit formula. We 
consider
two reflected Brownian motions in $D$, driven by the same Brownian 
motion
(i.e., a `synchronous coupling'). If $\Lambda(D)>0$ then the distance 
between
the two Brownian particles goes to 0 exponentially fast with rate 
$\Lambda
(D)/(2|D|)$ as time goes to infinity. The exponent $\Lambda(D)$ is 
strictly
positive if the domain has at most one hole. It is an open problem 
whether
there exists a domain with $\Lambda(D)<0$.


http://front.math.ucdavis.edu/math.PR/0501486

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3077. MEAN-FIELD DRIVEN FIRST-ORDER PHASE TRANSITIONS IN SYSTEMS WITH  
LONG-RANGE INTERACTIONS

Marek Biskup and  Lincoln Chayes and  Nicholas Crawford

We consider a class of spin systems on $\Z^d$ with vector valued spins
$(S_x)$ that interact via the pair-potentials $J_{x,y}S_x\cdot S_y$. The
interactions are generally spread-out in the sense that the $J_{x,y}$'s 
exhibit
either exponential or power-law fall-off. Under the technical condition 
of
reflection positivity and for sufficiently spread out interactions, we 
prove
that the model exhibits a first-order phase transition whenever the 
associated
mean-field theory signals such a transition. As a consequence, e.g., in
dimensions $d\ge3$, we can finally provide examples of the 3-state 
Potts model
with spread-out, exponentially decaying interactions, which undergoes a
first-order phase transition as the temperature varies. Similar 
transitions are
established in dimensions $d=1,2$ for power-law decaying interactions 
and in
high dimensions for next-nearest neighbor couplings. In addition, we 
also
investigate the limit of infinitely spread-out interactions. 
Specifically, we
show that once the mean-field theory is in a unique "state," then in any
sequence of translation-invariant Gibbs states various observables 
converge to
their mean-field values and the states themselves converge to product 
measure.


http://front.math.ucdavis.edu/math-ph/0501067

---------------------------------------------------------------

3078. GOLDBUG VARIATIONS

Michael Kleber

This "Mathematical Entertainments" column from the Intelligencer is an
exposition of current investigations, rooted in recent work of Jim 
Propp, into
"quasirandom" analogues of random walk and random aggregation processes.
Featured are the "Goldbugs" and the "Rotor-router". These are 
deterministic
processes which simulate the random ones, for example having the same 
limiting
states, but with faster convergence.
   The paper includes three large illustrations, which appear twice in 
the
submission, as both raster image (.png) and postscript (.eps) files. 
The latter
are much larger but needed for latex inclusion; the former are smaller, 
used by
pdflatex, and better for pixel-level viewing.


http://front.math.ucdavis.edu/math.CO/0501497

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3079. IDENTITIES IN LAW BETWEEN QUADRATIC FUNCTIONALS OF BIVARIATE 
GAUSSIAN  PROCESSES, THROUGH FUBINI THEOREMS AND SYMMETRIC PROJECTIONS

Giovanni Peccati (LSTA) and  Marc Yor (PMA)

We present three new identities in law for quadratic functionals of
conditioned bivariate Gaussian processes. In particular, our results 
provide a
two-parameter generalization of a celebrated identity in law, involving 
the
path variance of a Brownian bridge, due to Watson (1961). The proof is 
based on
ideas from a recent note by J. R. Pycke (2005) and on the stochastic 
Fubini
theorem for general Gaussian measures proved in Deheuvels et al. (2004).


http://front.math.ucdavis.edu/math.PR/0501506

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3080. THE MEAN SQUARE OF WEIGHTED MULTIPLICITIES FUNCTION

Lukianov Vladimir

We define a weighted multiplicity function for closed geodesics of given
length on a finite area Riemann surface. These weighted multiplicities 
appear
naturally in the Selberg trace formula, and in particular their mean 
square
plays an important role in the study of statistics of the eigenvalues 
of the
Laplacian on the surface.
     In the case of the modular domain, E. Bogomolny, F. Leyvraz and C. 
Schmit
gave a formula for the mean square, which was rigorously proved by M. 
Peter. In
this paper we calculate the mean square of weighted multiplicities for 
some
surfaces associated to congruence subgroups of the unit group of a 
rational
quaternion algebra, in particular for congruence subgroups of the 
modular
group. Remarkably, the result turns out to be a rational multiple of 
the mean
square for the modular domain.


http://front.math.ucdavis.edu/math.NT/0501519

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3081. CRITICAL PERCOLATION ON CERTAIN NON-UNIMODULAR GRAPHS

Yuval Peres and  Gabor Pete and  Ariel Scolnicov

An important conjecture in percolation theory is that almost surely no
infinite cluster exists in critical percolation on any transitive graph 
for
which the critical probability is less than 1. Earlier work has 
established
this for the amenable cases Z^2 and Z^d for large d, as well as for all
non-amenable graphs with unimodular automorphism groups. We show that 
the
conjecture holds for several classes of non-amenable graphs with 
non-unimodular
automorphism groups: for decorated trees, for the non-unimodular 
Diestel-Leader
graphs, and for direct products of these graphs with an arbitrary 
transitive
graph. We also show that, in any of these graphs, the connection 
probability
between two vertices decay exponentially in their distance. Finally, we 
prove
that critical percolation on the positive part of the lamplighter group 
has no
infinite clusters.


http://front.math.ucdavis.edu/math.PR/0501532

---------------------------------------------------------------

3082. SHORTEST SPANNING TREES AND A COUNTEREXAMPLE FOR RANDOM WALKS IN 
RANDOM  ENVIRONMENTS

Maury Bramson and  Ofer Zeitouni and  Martin P. W. Zerner

We construct forests spanning $\Z^d, d\geq 2,$ that are stationary and
directed, and whose trees are infinite but are as short as possible. 
For $d\geq
3$, two independent copies of such forests, pointing into opposite 
directions,
can be pruned so as to become disjoint. From this, we construct in 
$d\geq 3$ a
stationary, polynomially mixing and uniformly elliptic environment of
nearest-neighbor transition probabilities on $\Z^d$, for which the
corresponding random walk (RWRE) disobeys a certain zero-one law for
directional transience.


http://front.math.ucdavis.edu/math.PR/0501533

---------------------------------------------------------------

3083. SINGULAR CONTROL WITH STATE CONSTRAINTS ON UNBOUNDED DOMAIN

Rami Atar and Amarjit Budhiraja

We study a class of stochastic control problems where a cost of the form
\E\int_{[0,\infty)}e^{-\beta s}[\ell(X_s)ds+h(Y^\circ_s)d|Y|_s] is to be
minimized over control processes Y whose increments take values in a 
cone \YY
of \R^p, keeping the state process X=x+B+GY in a cone \bS of \R^k, k\le 
p.
Here, x\in\bS, B is a Brownian motion with drift b and covariance 
\Sigma, G is
a fixed matrix, and Y^\circ is the Radon-Nikodym derivative dY/d|Y|. Let
\calL=-(1/2)\trace(\Sig D^2)-b\cd D where D denotes the gradient. 
Solutions to
the corresponding dynamic programming PDE [(\calL+\beta) f-\ell]
\vee\sup_{y\in\YY:|Gy|=1}[-Gy\cd Df - h(y)]=0, on \bS^o are considered 
with a
polynomial growth condition and are required to be supersolution up to 
the
boundary (corresponding to a ``state constraint'' boundary condition on
\pl\XX). Under suitable conditions on the problem data, including 
continuity
and nonnegativity of \ell and h, and polynomial growth of \ell, our 
main result
is the unique viscosity-sense solvability of the PDE by the control 
problem's
value function in appropriate classes of functions. In some cases where
uniqueness generally fails to hold in the class of functions that grow 
at most
polynomially (e.g., when h=0), our methods provide uniqueness within 
the class
of functions that, in addition, have compact level sets. The results 
are new
even in the following special cases: (1) The one-dimensional case k=p=1,
\bS=\YY=\R_+; (2) The first order case \Sigma=0; (3) The case where 
\ell and h
are linear. The proofs combine probabilistic arguments and viscosity 
solution
methods. Our framework covers a wide range of diffusion control 
problems that
arise from queueing networks in heavy traffic.


http://front.math.ucdavis.edu/math.PR/0501016

---------------------------------------------------------------

3084. ON L\'{E}VY PROCESSES CONDITIONED TO STAY POSITIVE

Lo\"{i}c Chaumont (LPMA) and  Ron A. Doney

We construct the law of L\'{e}vy processes conditioned to stay positive 
under
general hypotheses. We obtain a Williams type path decomposition at the 
minimum
of these processes. This result is then applied to prove the weak 
convergence
of the law of L\'{e}vy processes conditioned to stay positive as their 
initial
state tends to 0. We describe an absolute continuity relationship 
between the
limit law and the measure of the excursions away from 0 of the 
underlying
L\'{e}vy process reflected at its minimum. Then, when the L\'{e}vy 
process
creeps upwards, we study the lower tail at 0 of the law of the height 
this
excursion.


http://front.math.ucdavis.edu/math.PR/0502012

---------------------------------------------------------------

3085. THE MAXIMUM ENTROPY STATE

Keye Martin

We give an algorithm for calculating the maximum entropy state as the 
least
fixed point of a Scott continuous mapping on the domain of classical 
states in
their Bayesian order.


http://front.math.ucdavis.edu/math.PR/0502024

---------------------------------------------------------------

3086. PROOF OF THE LOCAL REM CONJECTURE FOR NUMBER PARTITIONING

Christian Borgs and  Jennifer Chayes and  Stephan Mertens and Chandra 
Nair

The number partitioning problem is a classic problem of combinatorial
optimization in which a set of $n$ numbers is partitioned into two 
subsets such
that the sum of the numbers in one subset is as close as possible to 
the sum of
the numbers in the other set. When the $n$ numbers are i.i.d. variables 
drawn
from some distribution, the partitioning problem turns out to be 
equivalent to
a mean-field antiferromagnetic Ising spin glass. In the spin glass
representation, it is natural to define energies -- corresponding to 
the costs
of the partitions, and overlaps -- corresponding to the correlations 
between
partitions. Although the energy levels of this model are {\em a priori} 
highly
correlated, a surprising recent conjecture asserts that the energy 
spectrum of
number partitioning is locally that of a random energy model (REM): the
spacings between nearby energy levels are uncorrelated. In other words, 
the
properly scaled energies converge to a Poisson process. The conjecture 
also
asserts that the corresponding spin configurations are uncorrelated, 
indicating
vanishing overlaps in the spin glass representation. In this paper, we 
prove
these two claims, collectively known as the local REM conjecture.


http://front.math.ucdavis.edu/cond-mat/0501760

---------------------------------------------------------------

3087. A SHARP INEQUALITY FOR CONDITIONAL DISTRIBUTION OF THE FIRST EXIT 
TIME  OF BROWNIAN MOTION

Majid Hosseini

Let $U$ be a domain, convex in $x$ and symmetric about the y-axis, 
which is
contained in a centered and oriented rectangle $R$. \linebreak If 
$\tau_A$ is
the first exit time of Brownian motion from $A$ and $A^+=A\cap 
\{(x,y):x>0\}$,
it is proved that $P^z(\tau_{U^+}>s\mid \tau_{R^+}>t)\leq 
P^z(\tau_{U}>s\mid
\tau_{R}>t)$ for every $s,t>0$ and every $z\in U^+$.


http://front.math.ucdavis.edu/math.PR/0502057

---------------------------------------------------------------

3088. ON POSITIVE RECURRENCE OF CONSTRAINED DIFFUSION PROCESSES

Rami Atar and  Amarjit Budhiraja and P. Dupuis

Let G \subset \R^k be a convex polyhedral cone with vertex at the origin
given as the intersection of half spaces {G_i, i= 1, ..., N}, where n_i 
and d_i
denote the inward normal and direction of constraint associated with 
G_i,
respectively. Stability properties of a class of diffusion processes,
constrained to take values in G, are studied under the assumption that 
the
Skorokhod problem defined by the data {(n_i, d_i), i = 1, ..., N} is 
well posed
and the Skorokhod map is Lipschitz continuous. Explicit conditions on 
the drift
coefficient, b(\cdot), of the diffusion process are given under which 
the
constrained process is positive recurrent and has a unique invariant 
measure.
Define \C \Df{- \sum_{i=1}^N \alpha_i d_i; \alpha_i \ge 0, i \in \{1, 
..., N}}.
Then the key condition for stability is that there exists \delta \in (0,
\infty) and a bounded subset A of G such that for all x \in G\backslash 
A, b(x)
\in \C and \dist(b(x), \partial \C) \ge \delta, where \partial \C 
denotes the
boundary of \C.


http://front.math.ucdavis.edu/math.PR/0501018

---------------------------------------------------------------

3089. ON LARGE DEVIATIONS IN THE AVERAGING PRINCIPLE FOR SDE'S WITH A 
``FULL  DEPENDENCE'', CORRECTION

Alexander Yu. Veretennikov

We establish the large deviation principle for stochastic differential
equations with averaging in the case when all coefficients of the fast
component depend on the slow one, including diffusion.


http://front.math.ucdavis.edu/math.PR/0502098

---------------------------------------------------------------

3090. NONPARAMETRIC REGRESSION ESTIMATION FOR RANDOM FIELDS IN A 
FIXED-DESIGN

Mohamed El Machkouri (LMRS)

We investigate the nonparametric estimation for regression in a 
fixed-design
setting when the errors are given by a field of dependent random 
variables.
Sufficient conditions for kernel estimators to converge uniformly are 
obtained.
These estimators can attain the optimal rates of uniform convergence 
and the
results apply to a large class of random fields which contains
martingale-difference random fields and mixing random fields.


http://front.math.ucdavis.edu/math.ST/0502091

---------------------------------------------------------------

3091. ON THE ASYMPTOTIC BEHAVIOR OF SOME ALGORITHMS

Philippe Robert (RAP UR-R)

A simple approach is presented to study the asymptotic behavior of some
algorithms with an underlying tree structure. It is shown that some 
asymptotic
oscillating behaviors can be precisely analyzed without resorting to 
complex
analysis techniques as it is usually done in this context. A new 
explicit
representation of periodic functions involved is obtained at the same 
time.


http://front.math.ucdavis.edu/cs.DS/0502014

---------------------------------------------------------------

3092. ON LARGE DEVIATIONS IN THE AVERAGING PRINCIPLE FOR SDE'S WITH A 
``FULL  DEPENDENCE'', CORRECTION

Alexander Yu. Veretennikov

We establish the large deviation principle for stochastic differential
equations with averaging in the case when all coefficients of the fast
component depend on the slow one, including diffusion.


http://front.math.ucdavis.edu/math.PR/0502098

---------------------------------------------------------------

3093. NONPARAMETRIC REGRESSION ESTIMATION FOR RANDOM FIELDS IN A 
FIXED-DESIGN

Mohamed El Machkouri (LMRS)

We investigate the nonparametric estimation for regression in a 
fixed-design
setting when the errors are given by a field of dependent random 
variables.
Sufficient conditions for kernel estimators to converge uniformly are 
obtained.
These estimators can attain the optimal rates of uniform convergence 
and the
results apply to a large class of random fields which contains
martingale-difference random fields and mixing random fields.


http://front.math.ucdavis.edu/math.ST/0502091

---------------------------------------------------------------

3094. ON THE ASYMPTOTIC BEHAVIOR OF SOME ALGORITHMS

Philippe Robert (RAP UR-R)

A simple approach is presented to study the asymptotic behavior of some
algorithms with an underlying tree structure. It is shown that some 
asymptotic
oscillating behaviors can be precisely analyzed without resorting to 
complex
analysis techniques as it is usually done in this context. A new 
explicit
representation of periodic functions involved is obtained at the same 
time.


http://front.math.ucdavis.edu/cs.DS/0502014

---------------------------------------------------------------

3095. PROPERTIES OF THE WEALTH PROCESS IN A MARKET MICROSTRUCTURE MODEL

Ted Theodosopoulos and Ming Yuen

In this short paper we define the wealth process in a spin model for 
market
microstructure, for individual agents and in aggregate. The agents in 
our model
try to balance their desire to belong to the local majority (herding 
behavior),
defined over random network neighborhoods, and the occasional advantage 
of
belonging to the global minority (contrarian trading). We arrive at a
classification of the martingale properties of this wealth process and 
use it
to determine the strategic stability of the agents' interactions. Our 
goal is
to add a behavioral interpretation to this stochastic agent-based model 
for
market fluctuations.


http://front.math.ucdavis.edu/math.PR/0502105

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3096. DIFFERENT ASPECTS OF A MODEL FOR RANDOM FRAGMENTATION PROCESSES

Jean Bertoin (PMA)

This text surveys different probabilistic aspects of a model which is 
used to
describe the evolution of an object that falls apart randomly as time 
passes.
Each point of view yields useful techniques to establish properties of 
such
random fragmentation processes.


http://front.math.ucdavis.edu/math.PR/0502132

---------------------------------------------------------------

3097. INVARIANCE PRINCIPLES FOR STANDARD-NORMALIZED AND SELF-NORMALIZED 
RANDOM  FIELDS

Mohamed El Machkouri (LMRS) and  Lahcen Ouchti (LMRS)

We investigate the invariance principle for set-indexed partial sums of 
a
stationary field $(X\_{k})\_{k\in\mathbb{Z}^{d}}$ of 
martingale-difference or
independent random variables under standard-normalization or 
self-normalization
respectively.


http://front.math.ucdavis.edu/math.PR/0502135

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3098. PINNING OF POLYMERS AND INTERFACES BY RANDOM POTENTIALS

Kenneth S. Alexander and Vladas Sidoravicius

We consider a polymer, with monomer locations modeled by the trajectory 
of a
Markov chain, in the presence of a potential that interacts with the 
polymer
when it visits a particular site 0. Disorder is introduced by, for 
example,
having the interaction vary from one monomer to another, as a constant 
$u$ plus
i.i.d. mean-0 randomness. There is a critical value of $u$ above which 
the
polymer is pinned, placing a positive fraction of its monomers at 0 
with high
probability. This critical point may differ for the quenched, annealed 
and
deterministic cases. We show that self-averaging occurs, we evaluate the
critical point for a deterministic interaction and establish our main 
result
that the critical point in the quenched case is strictly smaller. We 
show that
for every fixed $u \in \mathbb{R}$, pinning occurs at sufficiently low
temperatures. If the excursion length distribution has polynomial tails 
and the
interaction does not have a finite exponential moment, then pinning 
occurs for
all $u \in \mathbb{R}$ at arbitrary temperature. Our results apply to 
other
mathematically similar situations as well, such as a directed polymer 
that
interacts with a random potential located in a one-dimensional defect, 
or an
interface in two dimensions interacting with a random potential along a 
wall.


http://front.math.ucdavis.edu/math.PR/0501028

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3099. TAKING BIGGER METROPOLIS STEPS BY DRAGGING FAST VARIABLES

Radford M. Neal

I show how Markov chain sampling with the Metropolis-Hastings algorithm 
can
be modified so as to take bigger steps when the distribution being 
sampled from
has the characteristic that its density can be quickly recomputed for a 
new
point if this point differs from a previous point only with respect to 
a subset
of 'fast' variables. I show empirically that when using this method, the
efficiency of sampling for the remaining 'slow' variables can approach 
what
would be possible using Metropolis updates based on the marginal 
distribution
for the slow variables.


http://front.math.ucdavis.edu/math.ST/0502099

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3100. A TWO ARMED BANDIT TYPE PROBLEM REVISITED

Gilles Pag\`{e}s (PMA)

In a recent paper, M. Bena\"{i}m and G. Ben Arous solve a multi-armed 
bandit
problem arising in the theory of learning in games. We propose an short
elementary proof of this result based on a variant of the Kronecker 
Lemma.


http://front.math.ucdavis.edu/math.PR/0502182

---------------------------------------------------------------

3101. ON THE HEDGING OF AMERICAN OPTIONS IN DISCRETE TIME MARKETS WITH  
PROPORTIONAL TRANSACTION COSTS

Bruno Bouchard (PMA) and  Emmanuel Temam (PMA)

In this note, we consider a general discrete time financial market with
proportional transaction costs as in Kabanov and Stricker (2001), 
Kabanov et
al. (2002), Kabanov et al. (2003) and Schachermayer (2004). We provide 
a dual
formulation for the set of initial endowments which allow to 
super-hedge some
American claim. We show that this extends the result of Chalasani and 
Jha
(2001) which was obtained in a model with constant transaction costs 
and risky
assets which evolve on a finite dimensional tree. We also provide fairly
general conditions under which the expected formulation in terms of 
stopping
times does not work.


http://front.math.ucdavis.edu/math.PR/0502189

---------------------------------------------------------------

3102. ON MAXIMA AND LADDER PROCESSES FOR A DENSE CLASS OF LEVY PROCESSES

M. R. Pistorius

Consider the problem to explicitly calculate the law of the first 
passage
time T(a) of a general Levy process Z above a positive level a. In this 
paper
it is shown that the law of T(a) can be approximated arbitrarily 
closely by the
laws of T^n(a), the corresponding first passages time for X^n, where 
(X^n)_n is
a sequence of Levy processes whose positive jumps follow a phase-type
distribution. Subsequently, explicit expressions are derived for the 
laws of
T^n(a) and the upward ladder process of X^n.
   The derivation is based on an embedding of X^n into a class of Markov
additive processes and on the solution of the fundamental (matrix) 
Wiener-Hopf
factorisation for this class.
   This Wiener-Hopf factorisation can be computed explicitly by solving
iteratively a certain fixed point equation. It is shown that, 
typically, this
iteration converges geometrically fast.


http://front.math.ucdavis.edu/math.PR/0502192

---------------------------------------------------------------

3103. TWO-DIMENSIONAL WETTING WITH BINARY DISORDER: A NUMERICAL STUDY 
OF THE  LOOP STATISTICS

Thomas Garel and Cecile Monthus

We numerically study the wetting (adsorption) transition of a polymer 
chain
on a disordered substrate in 1+1 dimension.Following the 
Poland-Scheraga model
of DNA denaturation, we use a Fixman-Freire scheme for the entropy of 
loops.
This allows us to consider chain lengths of order $N \sim 10^5 $ to 
$10^6$,
with $10^4$ disorder realizations. Our study is based on the statistics 
of
loops between two contacts with the substrate, from which we define 
Binder-like
parameters: their crossings for various sizes $N$ allow a precise 
determination
of the critical temperature, and their finite size properties yields a
crossover exponent $\phi=1/(2-\alpha) \simeq 0.5$.We then analyse at
criticality the distribution of loop length $l$ in both regimes $l \sim 
O(N)$
and $1 \ll l \ll N$, as well as the finite-size properties of the 
contact
density and energy. Our conclusion is that the critical exponents for 
the
thermodynamics are the same as those of the pure case, except for strong
logarithmic corrections to scaling. The presence of these logarithmic
corrections in the thermodynamics is related to a disorder-dependent
logarithmic singularity that appears in the critical loop distribution 
in the
rescaled variable $\lambda=l/N$ as $\lambda \to 1$.


http://front.math.ucdavis.edu/cond-mat/0502195

---------------------------------------------------------------

3104. DEGREE DISTRIBUTION OF COMPETITION-INDUCED PREFERENTIAL 
ATTACHMENT  GRAPHS

N. Berger and  C. Borgs and  J. T. Chayes and  R. M. D'Souza and  R. D. 
Kleinberg

We introduce a family of one-dimensional geometric growth models, 
constructed
iteratively by locally optimizing the tradeoffs between two competing 
metrics,
and show that this family is equivalent to a family of preferential 
attachment
random graph models with upper cutoffs. This is the first explanation 
of how
preferential attachment can arise from a more basic underlying 
mechanism of
local competition. We rigorously determine the degree distribution for 
the
family of random graph models, showing that it obeys a power law up to 
a finite
threshold and decays exponentially above this threshold.
   We also rigorously analyze a generalized version of our graph 
process, with
two natural parameters, one corresponding to the cutoff and the other a
``fertility'' parameter. We prove that the general model has a 
power-law degree
distribution up to a cutoff, and establish monotonicity of the power as 
a
function of the two parameters. Limiting cases of the general model 
include the
standard preferential attachment model without cutoff and the uniform
attachment model.


http://front.math.ucdavis.edu/cond-mat/0502205

---------------------------------------------------------------

3105. ON NONEXISTENCE OF NON-CONSTANT VOLATILITY IN THE BLACK-SCHOLES 
FORMULA

K. Hamza and F.C. Klebaner

We prove that if the Black-Scholes formula holds with the spot 
volatility for
call options with all strikes, then the volatility parameter is 
constant. The
proof relies some result on semimartingales (Theorem 2) of independent
interest.


http://front.math.ucdavis.edu/math.PR/0502201

---------------------------------------------------------------

3106. MARTINGALE STRUCTURE OF SKOROHOD INTEGRAL PROCESSES

Giovanni Peccati (LSTA) and  Mich\`{e}le Thieullen (PMA) and  Ciprian 
A. Tudor  (SAMOS)

Let the process Y(t) be a Skorohod integral process with respect to 
Brownian
motion. We use a recent result by Tudor (2004), to prove that Y(t) can 
be
represented as the limit of linear combinations of processes that are 
products
of forward and backward Brownian martingales. Such a result is a 
further step
towards the connection between the theory of continuous-time 
(semi)martingales,
and that of anticipating stochastic integration. We establish an 
explicit link
between our results and the classic characterization, due to Duc and 
Nualart
(1990), of the chaotic decomposition of Skorohod integral processes. We 
also
explore the case of Skorohod integral processes that are time-reversed 
Brownian
martingales, and provide an "anticipating" counterpart to the classic 
Optional
Sampling Theorem for It\^{o} stochastic integrals.


http://front.math.ucdavis.edu/math.PR/0502208

---------------------------------------------------------------

3107. ASYMPTOTICS IN KNUTH'S PARKING PROBLEM FOR CARAVANS

Jean Bertoin (PMA) and  Gr\'{e}gory Marc Miermont (LM-Orsay)

We consider a generalized version of Knuth's parking problem, in which
caravans consisting of a number of cars arrive at random on the unit 
circle.
Then each car turns clockwise until it finds a free space to park. 
Extending a
recent work by Chassaing and Louchard, we relate the asymptotics for 
the sizes
of blocks formed by occupied spots with the dynamics of the additive
coalescent. According to the behavior of the caravan's size tail 
distribution,
several qualitatively different versions of eternal additive coalescent 
are
involved.


http://front.math.ucdavis.edu/math.PR/0502220

---------------------------------------------------------------

3108. AN ESCAPE TIME CRITERION FOR QUEUEING NETWORKS: ASYMPTOTIC  
RISK-SENSITIVE CONTROL VIA DIFFERENTIAL GAMES

Rami Atar and  Paul Dupuis and Adam Shwartz

We consider the problem of risk-sensitive control of a stochastic 
network. In
controlling such a network, an escape time criterion can be useful if 
one
wishes to regulate the occurrence of large buffers and buffer overflow. 
In this
paper a risk-sensitive escape time criterion is formulated, which in 
comparison
to the ordinary escape time criteria penalizes exits which occur on 
short time
intervals more heavily. The properties of the risk-sensitive problem are
studied in the large buffer limit, and related to the value of a 
deterministic
differential game with constrained dynamics. We prove that the game has 
value,
and that the value is the (viscosity) solution of a PDE. For a simple 
network,
the value is computed, demonstrating the applicability of the approach.


http://front.math.ucdavis.edu/math.PR/0501031

---------------------------------------------------------------

3109. ABSOLUTE CONTINUITY FOR RANDOM ITERATED FUNCTION SYSTEMS WITH 
OVERLAPS

Yuval Peres and  K\'aroly Simon and  Boris Solomyak

We consider linear iterated function systems with a random 
multiplicative
error on the real line. Our system is $\{x\mapsto d_i + \lambda_i Y
x\}_{i=1}^m$, where $d_i\in \R$ and $\lambda_i>0$ are fixed and $Y> 0$ 
is a
random variable with an absolutely continuous distribution. The 
iterated maps
are applied randomly according to a stationary ergodic process, with the
sequence of i.i.d. errors $y_1,y_2,...$, distributed as $Y$, 
independent of
everything else. Let $h$ be the entropy of the process, and let $\chi =
E[\log(\lambda Y)]$ be the Lyapunov exponent. Assuming that $\chi < 0$, 
we
obtain a family of conditional measures $\nu_y$ on the line, 
parametrized by $y
= (y_1,y_2,...)$, the sequence of errors. Our main result is that if $h 
 >
|\chi|$, then $\nu_y$ is absolutely continuous with respect to the 
Lebesgue
measure for a.e. $y$. We also prove that if $h < |\chi|$, then the 
measure
$\nu_y$ is singular and has dimension $h/|\chi|$ for a.e. $y$. These 
results
are applied to a randomly perturbed IFS suggested by Y. Sinai, and to a 
class
of random sets considered by R. Arratia, motivated by probabilistic 
number
theory.


http://front.math.ucdavis.edu/math.DS/0502200

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3110. SUBTREE PRUNE AND RE-GRAFT: A REVERSIBLE REAL TREE VALUED MARKOV 
PROCESS

Steven N. Evans and Anita Winter

We use Dirichlet form methods to construct and analyze a reversible 
Markov
process, the stationary distribution of which is the Brownian continuum 
random
tree. This process is inspired by the subtree prune and re-graft (SPR) 
Markov
chains that appear in phylogenetic analysis. A key technical ingredient 
in this
work is the use of a novel Gromov--Hausdorff type distance to metrize 
the space
whose elements are compact real trees equipped with a probability 
measure.
Also, the investigation of the Dirichlet form hinges on a new path
decomposition of the Brownian excursion.


http://front.math.ucdavis.edu/math.PR/0502226

---------------------------------------------------------------

3111. INDIVIDUAL DISPLACEMENTS IN HASHING WITH COALESCED CHAINS

Svante Janson

We study the asymptotic distribution of the displacements in hashing 
with
coalesced chains, for both late-insertion and early-insertion. 
Asymptotic
formulas for means and variances follow. The method uses Poissonization 
and
some stochastic calculus.


http://front.math.ucdavis.edu/math.PR/0502232

---------------------------------------------------------------

3112. RANDOM RECURSIVE TREES AND THE BOLTHAUSEN-SZNITMAN COALESCENT

Christina Goldschmidt and James B. Martin

We describe a representation of the Bolthausen-Sznitman coalescent in 
terms
of the cutting of random recursive trees. Using this representation, we 
prove
results concerning the final collision of the coalescent restricted to 
[n]: we
show that the distribution of the number of blocks involved in the final
collision converges as n tends to infinity, and obtain a scaling law 
for the
sizes of these blocks. We also consider the discrete-time Markov chain 
giving
the number of blocks after each collision of the coalescent restricted 
to [n];
we show that the transition probabilities of the time-reversal of this 
Markov
chain have limits as n tends to infinity. These results can be 
interpreted as
describing a ``post-gelation'' phase of the Bolthausen-Sznitman 
coalescent, in
which a giant cluster containing almost all of the mass has already 
formed and
the remaining small blocks are being absorbed.


http://front.math.ucdavis.edu/math.PR/0502263

---------------------------------------------------------------

3113. THE LINKING PROBABILITY OF DEEP SPIDER-WEB NETWORKS

Nicholas Pippenger

We consider crossbar switching networks with base $b$ (that is, 
constructed
from $b\times b$ crossbar switches), scale $k$ (that is, with $b^k$ 
inputs,
$b^k$ outputs and $b^k$ links between each consecutive pair of stages) 
and
depth $l$ (that is, with $l$ stages). We assume that the crossbars are
interconnected according to the spider-web pattern, whereby two 
diverging paths
reconverge only after at least $k$ stages. We assume that each vertex is
independently idle with probability $q$, the vacancy probability. We 
assume
that $b\ge 2$ and the vacancy probability $q$ are fixed, and that $k$ 
and $l =
ck$ tend to infinity with ratio a fixed constant $c>1$. We consider the 
linking
probability $Q$ (the probability that there exists at least one idle 
path
between a given idle input and a given idle output). In a previous 
paper it was
shown that if $c\le 2$, then the linking probability $Q$ tends to 0 if
$0<q<q_c$ (where $q_c = 1/b^{(c-1)/c}$ is the critical vacancy 
probability),
and tends to $(1-\xi)^2$ (where $\xi$ is the unique solution of the 
equation
$(1-q (1-x))^b=x$ in the range $0<x<1$) if $q_c<q<1$. In this paper we 
extend
this result to all rational $c>1$. This is done by using generating 
functions
and complex-variable techniques to estimate the second moments of 
various
random variables involved in the analysis of the networks.


http://front.math.ucdavis.edu/math.PR/0502294

---------------------------------------------------------------

3114. EXPLICIT SOLUTION FOR A NETWORK CONTROL PROBLEM IN THE LARGE 
DEVIATION  REGIME

Rami Atar and  Paul Dupuis and Adam Shwartz

We consider optimal control of a stochastic network,where service is
controlled to prevent buffer overflow. We use a risk-sensitive escape 
time
criterion, which in comparison to the ordinary escape time criteria 
heavily
penalizes exits which occur on short time intervals. A limit as the 
buffer
sizes tend to infinity is considered. In [2] we showed that, for a 
large class
of networks, the limit of the normalized cost agrees with the value 
function of
a differential game. The game's value is characterized in [2] as the 
unique
solution to a Hamilton-Jacobi-Bellman Partial Differential Equation 
(PDE). In
the current paper we apply this general theory to the important case of 
a
network of queues in tandem. Our main results are: (i) the construction 
of an
explicit solution to the corresponding PDE, and (ii) drawing out the
implications for optimal risk-sensitive and robust regulation of the 
network.
In particular, the following general principle can be extracted. To 
avoid
buffer overflow there is a natural competition between two tendencies. 
One may
choose to serve a particular queue, since that will help prevent its 
own buffer
from overflowing, or one may prefer to stop service, with the goal of
preventing overflow of buffers further down the line. The solution to 
the PDE
indicates the optimal choice between these two, specifying the parts of 
the
state space where each queue must be served (so as not to lose 
optimality), and
where it can idle.


http://front.math.ucdavis.edu/math.PR/0501035

---------------------------------------------------------------

3115. ESTIMATES ON PATH DELOCALIZATION FOR COPOLYMERS AT SELECTIVE 
INTERFACES

Giambattista Giacomin and  Fabio Lucio Toninelli

We consider a directed random walk model of a random heterogeneous 
polymer in
the proximity of an interface separating two selective solvents. This 
model
exhibits a localization/delocalization transition. A positive value of 
the free
energy corresponds to the localized regime and strong results on the 
polymer
path behavior are known in this case. We focus on the interior of the
delocalized phase, which is characterized by the free energy equal to 
zero, and
we show in particular that in this regime there are O(log N) monomers 
in the
unfavorable solvent (N is the length of the polymer). The previously 
known
result was o(N). Our approach is based on concentration bounds on 
suitably
restricted partition functions. The same idea allows also to interpolate
between different types of disorder in the weak coupling limit. In this 
way we
show the universal nature of this limit, previously considered only for 
binary
disorder.


http://front.math.ucdavis.edu/math.PR/0502304

---------------------------------------------------------------

3116. SOME PROPERTIES OF THE RATE FUNCTION OF QUENCHED LARGE DEVIATIONS 
FOR  RANDOM WALK IN RANDOM ENVIRONMENT

Alexis Devulder (PMA)

In this paper, we are interested in some questions of Greven and den
Hollander about the rate function $I\_{\eta}^q$ of quenched large 
deviations
for random walk in random environment. By studying the hitting times of 
RWRE,
we prove that in the recurrent case, $\lim\_{\theta\to
0^+}(I\_{\eta}^q)''(\theta)=+\infty$, which gives an affirmative answer 
to a
conjecture of Greven and den Hollander. We also establish a comparison 
result
between the rate function of quenched large deviations for a diffusion 
in a
drifted Brownian potential, and the rate function for a drifted 
Brownian motion
with the same speed.


http://front.math.ucdavis.edu/math.PR/0502316

---------------------------------------------------------------

3117. AN ADAPTIVE SCHEME FOR THE APPROXIMATION OF DISSIPATIVE SYSTEMS

Vincent Lemaire

We propose a new scheme for the long time approximation of a diffusion 
when
the drift vector field is not globally Lipschitz. Under this assumption,
regular explicit Euler scheme --with constant or decreasing step-- may 
explode
and implicit Euler scheme are CPU-time expensive. The algorithm we 
introduce is
explicit and we prove that any weak limit of the weighted empirical 
measures of
this scheme is a stationary distribution of the stochastic differential
equation. Several examples are presented including gradient dissipative 
systems
and Hamiltonian dissipative systems.


http://front.math.ucdavis.edu/math.PR/0502317

---------------------------------------------------------------

3118. LIMIT LAWS FOR RANDOM VECTORS WITH AN EXTREME COMPONENT

J. Heffernan & S. Resnick

Models based on assumptions of multivariate regular variation and hidden
regular variation provide ways to describe a broad range of extremal 
dependence
structures when marginal distributions are heavy tailed. Multivariate 
regular
variation provides a rich description of extremal dependence in the 
case of
asymptotic dependence, but fails to distinguish between exact 
independence and
asymptotic independence. Hidden regular variation addresses this 
problem by
requiring components of the random vector to be simultaneously large 
but on a
smaller scale than the scale for the marginal distributions. In doing 
so,
hidden regular variation typically restricts attention to that part of 
the
probability space where all variables are simultaneously large. 
However, since
under asymptotic independence the largest values do not occur in the 
same
observation, the region where variables are simultaneously large may 
not be of
primary interest. A different philosophy was offered in the paper of 
Heffernan
and Tawn (2004) which allows examination of distributional tails other 
than the
joint tail. This approach used an asymptotic argument which conditions 
on one
component of the random vector and finds the limiting conditional 
distribution
of the remaining components as the conditioning variable becomes large. 
In this
paper, we provide a thorough mathematical examination of the limiting 
arguments
building on the orientation of Heffernan and Tawn (2004). We examine the
conditions required for the assumptions made by the conditioning 
approach to
hold, and highlight similarities and differences between the new and
established methods.


http://front.math.ucdavis.edu/math.PR/0502324

---------------------------------------------------------------

3119. STRONG ASYMPTOTIC ASSERTIONS FOR DISCRETE MDL IN REGRESSION AND  
CLASSIFICATION

Jan Poland and Marcus Hutter

We study the properties of the MDL (or maximum penalized complexity)
estimator for Regression and Classification, where the underlying model 
class
is countable. We show in particular a finite bound on the Hellinger 
losses
under the only assumption that there is a "true" model contained in the 
class.
This implies almost sure convergence of the predictive distribution to 
the true
one at a fast rate. It corresponds to Solomonoff's central theorem of 
universal
induction, however with a bound that is exponentially larger.


http://front.math.ucdavis.edu/math.ST/0502315

---------------------------------------------------------------

3120. ON THE OPERATOR SPACE UMD PROPERTY FOR NONCOMMUTATIVE LP-SPACES

Magdalena Musat

We study the operator space UMD property, introduced by Pisier in the 
context
of noncommutative vector-valued Lp-spaces. It is unknown whether the 
property
is independent of p in this setting. We prove that for 1<p,q<\infty, the
Schatten q-classes Sq are OUMDp. The proof relies on properties of the 
Haagerup
tensor product and complex interpolation. Using ultraproduct 
techniques, we
extend this result to a large class of noncommutative Lq-spaces. 
Namely, we
show that if M is a QWEP von Neumann algebra (i.e., a quotient of a 
C^*-algebra
with Lance's weak expectation property) equipped with a normal, faithful
tracial state \tau, then Lq(M,\tau) is OUMDp for 1<p,q<\infty.


http://front.math.ucdavis.edu/math.OA/0501033

---------------------------------------------------------------

3121. OPTIMALITY OF UNIVERSAL BAYESIAN SEQUENCE PREDICTION FOR GENERAL 
LOSS  AND ALPHABET

Marcus Hutter

Various optimality properties of universal sequence predictors based on
Bayes-mixtures in general, and Solomonoff's prediction scheme in 
particular,
will be studied. The probability of observing $x_t$ at time $t$, given 
past
observations $x_1...x_{t-1}$ can be computed with the chain rule if the 
true
generating distribution $\mu$ of the sequences $x_1x_2x_3...$ is known. 
If
$\mu$ is unknown, but known to belong to a countable or continuous 
class $\M$
one can base ones prediction on the Bayes-mixture $\xi$ defined as a
$w_\nu$-weighted sum or integral of distributions $\nu\in\M$. The 
cumulative
expected loss of the Bayes-optimal universal prediction scheme based on 
$\xi$
is shown to be close to the loss of the Bayes-optimal, but infeasible
prediction scheme based on $\mu$. We show that the bounds are tight and 
that no
other predictor can lead to significantly smaller bounds. Furthermore, 
for
various performance measures, we show Pareto-optimality of $\xi$ and 
give an
Occam's razor argument that the choice $w_\nu\sim 2^{-K(\nu)}$ for the 
weights
is optimal, where $K(\nu)$ is the length of the shortest program 
describing
$\nu$. The results are applied to games of chance, defined as a 
sequence of
bets, observations, and rewards. The prediction schemes (and bounds) are
compared to the popular predictors based on expert advice. Extensions to
infinite alphabets, partial, delayed and probabilistic prediction,
classification, and more active systems are briefly discussed.


http://front.math.ucdavis.edu/cs.LG/0311014

---------------------------------------------------------------

3122. ON THE CONVERGENCE SPEED OF MDL PREDICTIONS FOR BERNOULLI 
SEQUENCES

Jan Poland and Marcus Hutter

We consider the Minimum Description Length principle for online sequence
prediction. If the underlying model class is discrete, then the total 
expected
square loss is a particularly interesting performance measure: (a) this
quantity is bounded, implying convergence with probability one, and (b) 
it
additionally specifies a `rate of convergence'. Generally, for MDL only
exponential loss bounds hold, as opposed to the linear bounds for a 
Bayes
mixture. We show that this is even the case if the model class contains 
only
Bernoulli distributions. We derive a new upper bound on the prediction 
error
for countable Bernoulli classes. This implies a small bound (comparable 
to the
one for Bayes mixtures) for certain important model classes. The 
results apply
to many Machine Learning tasks including classification and hypothesis 
testing.
We provide arguments that our theorems generalize to countable classes 
of
i.i.d. models.


http://front.math.ucdavis.edu/cs.LG/0407039

---------------------------------------------------------------

3123. UNIVERSAL CONVERGENCE OF SEMIMEASURES ON INDIVIDUAL RANDOM 
SEQUENCES

Marcus Hutter and Andrej Muchnik

Solomonoff's central result on induction is that the posterior of a 
universal
semimeasure M converges rapidly and with probability 1 to the true 
sequence
generating posterior mu, if the latter is computable. Hence, M is 
eligible as a
universal sequence predictor in case of unknown mu. Despite some nearby 
results
and proofs in the literature, the stronger result of convergence for all
(Martin-Loef) random sequences remained open. Such a convergence result 
would
be particularly interesting and natural, since randomness can be 
defined in
terms of M itself. We show that there are universal semimeasures M 
which do not
converge for all random sequences, i.e. we give a partial negative 
answer to
the open problem. We also provide a positive answer for some 
non-universal
semimeasures. We define the incomputable measure D as a mixture over all
computable measures and the enumerable semimeasure W as a mixture over 
all
enumerable nearly-measures. We show that W converges to D and D to mu 
on all
random sequences. The Hellinger distance measuring closeness of two
distributions plays a central role.


http://front.math.ucdavis.edu/cs.LG/0407057

---------------------------------------------------------------

3124. FUNCTIONAL QUANTIZATION AND METRIC ENTROPY FOR RIEMANN-LIOUVILLE  
PROCESSES

Harald Luschgy and  Gilles Pag\`{e}s (PMA)

We derive a high-resolution formula for the $L^2$-quantization errors of
Riemann-Liouville processes and the sharp Kolmogorov entropy 
asymptotics for
related Sobolev balls. We describe a quantization procedure which leads 
to
asymptotically optimal functional quantizers. Regular variation of the
eigenvalues of the covariance operator plays a crucial role.


http://front.math.ucdavis.edu/math.PR/0502375

---------------------------------------------------------------

3125. SELF-OPTIMIZING AND PARETO-OPTIMAL POLICIES IN GENERAL 
ENVIRONMENTS  BASED ON BAYES-MIXTURES

Marcus Hutter

The problem of making sequential decisions in unknown probabilistic
environments is studied. In cycle $t$ action $y_t$ results in 
perception $x_t$
and reward $r_t$, where all quantities in general may depend on the 
complete
history. The perception $x_t$ and reward $r_t$ are sampled from the 
(reactive)
environmental probability distribution $\mu$. This very general setting
includes, but is not limited to, (partial observable, k-th order) Markov
decision processes. Sequential decision theory tells us how to act in 
order to
maximize the total expected reward, called value, if $\mu$ is known.
Reinforcement learning is usually used if $\mu$ is unknown. In the 
Bayesian
approach one defines a mixture distribution $\xi$ as a weighted sum of
distributions $\nu\in\M$, where $\M$ is any class of distributions 
including
the true environment $\mu$. We show that the Bayes-optimal policy 
$p^\xi$ based
on the mixture $\xi$ is self-optimizing in the sense that the average 
value
converges asymptotically for all $\mu\in\M$ to the optimal value 
achieved by
the (infeasible) Bayes-optimal policy $p^\mu$ which knows $\mu$ in 
advance. We
show that the necessary condition that $\M$ admits self-optimizing 
policies at
all, is also sufficient. No other structural assumptions are made on 
$\M$. As
an example application, we discuss ergodic Markov decision processes, 
which
allow for self-optimizing policies. Furthermore, we show that $p^\xi$ is
Pareto-optimal in the sense that there is no other policy yielding 
higher or
equal value in {\em all} environments $\nu\in\M$ and a strictly higher 
value in
at least one.


http://front.math.ucdavis.edu/cs.AI/0204040

---------------------------------------------------------------

3126. NO-ARBITRAGE IN DISCRETE-TIME MARKETS WITH PROPORTIONAL 
TRANSACTION  COSTS AND GENERAL INFORMATION STRUCTURE

Bruno Bouchard (PMA and  Crest and  Lfa)

We discuss the no-arbitrage conditions in a general framework for
discrete-time models of financial markets with proportional transaction 
costs
and general information structure. We extend the results of Kabanov and 
al.
(2002), Kabanov and al. (2003) and Schachermayer (2004) to the case 
where
bid-ask spreads are not known with certainty. In the "no-friction" 
case, we
retrieve the result of Kabanov and Stricker (2003).


http://front.math.ucdavis.edu/math.PR/0501045

---------------------------------------------------------------

3127. CONVERGENCE AND ERROR BOUNDS FOR UNIVERSAL PREDICTION OF 
NONBINARY  SEQUENCES

Marcus Hutter

Solomonoff's uncomputable universal prediction scheme $\xi$ allows to 
predict
the next symbol $x_k$ of a sequence $x_1...x_{k-1}$ for any Turing 
computable,
but otherwise unknown, probabilistic environment $\mu$. This scheme 
will be
generalized to arbitrary environmental classes, which, among others, 
allows the
construction of computable universal prediction schemes $\xi$. 
Convergence of
$\xi$ to $\mu$ in a conditional mean squared sense and with $\mu$ 
probability 1
is proven. It is shown that the average number of prediction errors 
made by the
universal $\xi$ scheme rapidly converges to those made by the best 
possible
informed $\mu$ scheme. The schemes, theorems and proofs are given for 
general
finite alphabet, which results in additional complications as compared 
to the
binary case. Several extensions of the presented theory and results are
outlined. They include general loss functions and bounds, games of 
chance,
infinite alphabet, partial and delayed prediction, classification, and 
more
active systems.


http://front.math.ucdavis.edu/cs.LG/0106036

---------------------------------------------------------------

3128. CONVERGENCE AND LOSS BOUNDS FOR BAYESIAN SEQUENCE PREDICTION

Marcus Hutter

The probability of observing $x_t$ at time $t$, given past observations
$x_1...x_{t-1}$ can be computed with Bayes' rule if the true generating
distribution $\mu$ of the sequences $x_1x_2x_3...$ is known. If $\mu$ is
unknown, but known to belong to a class $M$ one can base ones 
prediction on the
Bayes mix $\xi$ defined as a weighted sum of distributions $\nu\in M$. 
Various
convergence results of the mixture posterior $\xi_t$ to the true 
posterior
$\mu_t$ are presented. In particular a new (elementary) derivation of 
the
convergence $\xi_t/\mu_t\to 1$ is provided, which additionally gives 
the rate
of convergence. A general sequence predictor is allowed to choose an 
action
$y_t$ based on $x_1...x_{t-1}$ and receives loss $\ell_{x_t y_t}$ if 
$x_t$ is
the next symbol of the sequence. No assumptions are made on the 
structure of
$\ell$ (apart from being bounded) and $M$. The Bayes-optimal prediction 
scheme
$\Lambda_\xi$ based on mixture $\xi$ and the Bayes-optimal informed 
prediction
scheme $\Lambda_\mu$ are defined and the total loss $L_\xi$ of 
$\Lambda_\xi$ is
bounded in terms of the total loss $L_\mu$ of $\Lambda_\mu$. It is 
shown that
$L_\xi$ is bounded for bounded $L_\mu$ and $L_\xi/L_\mu\to 1$ for 
$L_\mu\to
\infty$. Convergence of the instantaneous losses are also proven.


http://front.math.ucdavis.edu/cs.LG/0301014

---------------------------------------------------------------

3129. BAYESIAN TREATMENT OF INCOMPLETE DISCRETE DATA APPLIED TO MUTUAL  
INFORMATION AND FEATURE SELECTION

Marcus Hutter and Marco Zaffalon

Given the joint chances of a pair of random variables one can compute
quantities of interest, like the mutual information. The Bayesian 
treatment of
unknown chances involves computing, from a second order prior 
distribution and
the data likelihood, a posterior distribution of the chances. A common
treatment of incomplete data is to assume ignorability and determine the
chances by the expectation maximization (EM) algorithm. The two 
different
methods above are well established but typically separated. This paper 
joins
the two approaches in the case of Dirichlet priors, and derives 
efficient
approximations for the mean, mode and the (co)variance of the chances 
and the
mutual information. Furthermore, we prove the unimodality of the 
posterior
distribution, whence the important property of convergence of EM to the 
global
maximum in the chosen framework. These results are applied to the 
problem of
selecting features for incremental learning and naive Bayes 
classification. A
fast filter based on the distribution of mutual information is shown to
outperform the traditional filter based on empirical mutual information 
on a
number of incomplete real data sets.


http://front.math.ucdavis.edu/cs.LG/0306126

---------------------------------------------------------------

3130. KOLMOGOROV-SINAI ENTROPY OF A GENERALIZED MARKOV SHIFT

Ivan Werner

In this paper we calculate Kolmogorov-Sinai entropy $h_M(S)$ of the
generalized Markov shift associated with a contractive Markov system 
(CMS)
\cite{Wer1} using the coding map constructed in \cite{Wer3}. We show 
that
\[h_M(S)=-\sum\limits_{e\in E}\int\limits_{K_{i(e)}} p_e\log p_ed\mu\] 
where
$\mu$ is a unique invariant Borel probability measure of the CMS. I. 
Werner,
Contractive Markov systems, J. London Math. Soc. (2005) 236-258. I. 
Werner,
Coding map for a contractive Markov system, Math. Proc. Camb. Phil. 
Soc. to
appear 140 (2), March 2006.


http://front.math.ucdavis.edu/math.DS/0502389

---------------------------------------------------------------

3131. GAUSSIAN FLUCTUATIONS FOR NON-HERMITIAN RANDOM MATRIX ENSEMBLES

B. Rider and  Jack W. Silverstein

Consider an ensemble of $N \times N$ non-Hermitian matrices in which all
entries are independent identically distributed complex random 
variables of
mean zero and absolute mean-square one. If the entry distributions also 
possess
bounded densities and finite $(4+\ep)$ moments, then Z.D. Bai has shown 
the
ensemble to satisfy the circular law: after scaling by a factor of 
$1/\sqrt{N}$
and letting $N \ra \infty$, the empirical measure of the eigenvalues 
converges
weakly to the uniform measure on the unit disk in the complex plane. In 
this
note we investigate fluctuations from the circular law in a more 
restrictive
class of non-Hermitian matrices for which higher moments of the entries 
obey a
growth condition. The main result is a central limit theorem for linear
statistics of type $X_N(f) = \sum_{k=1}^N f(\ld_k)$ where $\lambda_1,
\lambda_2, ..., \lambda_N$ denote the ensemble eigenvalues and the test
function $f$ is analytic on an appropriate domain.


http://front.math.ucdavis.edu/math.PR/0502400

---------------------------------------------------------------

3132. A REPERTOIRE FOR ADDITIVE FUNCTIONALS OF UNIFORMLY DISTRIBUTED 
M-ARY  SEARCH TREES

James Allen Fill and Nevin Kapur

Using recent results on singularity analysis for Hadamard products of
generating functions, we obtain the limiting distributions for additive
functionals on $m$-ary search trees on $n$ keys with toll sequence (i)
$n^\alpha$ with $\alpha \geq 0$ ($\alpha=0$ and $\alpha=1$ correspond 
roughly
to the space requirement and total path length, respectively); (ii) $\ln
\binom{n}{m-1}$, which corresponds to the so-called shape functional; 
and (iii)
$\mathbf{1}_{n=m-1}$, which corresponds to the number of leaves.


http://front.math.ucdavis.edu/math.PR/0502422

---------------------------------------------------------------

3133. PHASE TRANSITION FOR PARKING BLOCKS, BROWNIAN EXCURSION AND 
COALESCENCE

Philippe Chassaing (IEC) and  Guy Louchard (ULB)

In this paper, we consider hashing with linear probing for a hashing 
table
with m places, n items (n < m), and l = m<n empty places. For a non 
computer
science-minded reader, we shall use the metaphore of n cars parking on m
places: each car chooses a place at random, and if this place k is 
occupied,
the car tries successively k+1, k+2, ... until it finds an empty place 
(with
the convention that place m+1 is actually place 1). Pittel [42] proves 
that
when l/m goes to some positive limit a < 1, the size of the largest 
block of
consecutive cars is O(log m). In this paper we examine at which level 
for n a
phase transition occurs for the largest block of consecutive cars 
between o(m)
and O(m). The intermediate case reveals an interesting behaviour of 
sizes of
blocks, related to the standard additive coalescent in the same way as 
the
sizes of connected components of the random graph are related to the
multiplicative coalescent.


http://front.math.ucdavis.edu/math.PR/0501060

---------------------------------------------------------------

3134. HIGH RESOLUTION ASYMPTOTICS FOR THE ANGULAR BISPECTRUM OF 
SPHERICAL  RANDOM FIELDS

Domenico Marinucci

In this paper, we study the asymptotic behaviour of the angular 
bispectrum of
spherical random fields. Here, the asymptotic theory is developed in the
framework of fixed-radius fields, which are observed with increasing 
resolution
as the sample size grows. The results we present are then exploited in 
a set of
procedures aimed at testing non-Gaussianity; for these statistics, we 
are able
to show convergence to functionals of standard Brownian motion under 
the null
hypothesis. Analytic results are also presented on the behaviour of the 
tests
in the presence of a broad class of non-Gaussian alternatives. The 
issue of
testing for non-Gaussianity on spherical random fields has recently 
gained an
enormous empirical importance, especially in connection with the 
statistical
analysis of Cosmic Microwave Background radiation.


http://front.math.ucdavis.edu/math.PR/0502434

---------------------------------------------------------------

3135. COST-VOLUME RELATIONSHIPS FOR FLOWS THROUGH A DISORDERED NETWORK

David Aldous

In a network where the cost of flow across an edge is nonlinear in the 
volume
of flow, and where sources and destinations are uniform, one can 
consider the
relationship between total volume $v$ of flow through the network and 
the
minimum cost $c = Psi(v)$ of any flow with volume $v$. Under a simple
probability model (locally tree-like directed network, independent 
cost-volume
functions or different edges) we show how to compute $\Psi(v)$ in the
infinite-size limit. The argument uses a probabilistic reformulation of 
the
cavity method from statistical physics, and is not rigorous as 
presented here.
The methodology seems potentially useful for many problems concerning 
flows on
this class of random networks.


http://front.math.ucdavis.edu/cond-mat/0502346

---------------------------------------------------------------

3136. CONCERNING LIFE ANNUITIES

Leonhard Euler

This seems to be the first English translation of this paper from the 
French
original, ``Sur les rentes viageres''. In the paper, Euler gives a 
general
formula for calculating the price of a life annuity that yields a 
certain
amount per year, assuming the annuity manager can get a 5 percent 
return, for
people of different ages. He also gives formulas to calculate the price 
of
annuities that only start to pay out a certain number of years after 
they are
purchased. He gives many numerical examples, giving tables for the 
prices of
annuities for annuitants up to 90 years old.


http://front.math.ucdavis.edu/math.HO/0502421

---------------------------------------------------------------

3137. UNIVERSAL FINITARY CODES WITH EXPONENTIAL TAILS

Nate Harvey and  Alexander E. Holroyd and  Yuval Peres and  Dan Romik

In 1977, Keane and Smorodinsky showed that there exists a finitary
homomorphism from any finite-alphabet Bernoulli process to any other
finite-alphabet Bernoulli process of strictly lower entropy. In 1996, 
Serafin
proved the existence of a finitary homomorphism with finite expected 
coding
length. In this paper, we construct such a homomorphism in which the 
coding
length has exponential tails. Our construction is source-universal, in 
the
sense that it does not use any information on the source distribution 
other
than the alphabet size and a bound on the entropy gap between the 
source and
target distributions. We also indicate how our methods can be extended 
to prove
a source-specific version of the result for Markov chains.


http://front.math.ucdavis.edu/math.PR/0502484

---------------------------------------------------------------

3138. CONDITIONED BROWNIAN TREES

Jean-Francois Le Gall (ENS Paris) and  Mathilde Weill (ENS Paris)

We consider a Brownian tree consisting of a collection of 
one-dimensional
Brownian paths started from the origin, whose genealogical structure is 
given
by the Continuum Random Tree (CRT). This Brownian tree may be generated 
from
the Brownian snake driven by a normalized Brownian excursion, and thus 
yields a
convenient representation of the so-called Integrated Super-Brownian 
Excursion
(ISE), which can be viewed as the uniform probability measure on the 
tree of
paths. We discuss different approaches that lead to the definition of 
the
Brownian tree conditioned to stay on the positive half-line. We also 
establish
a Verwaat-like theorem showing that this conditioned Brownian tree can 
be
obtained by re-rooting the unconditioned one at the vertex 
corresponding to the
minimal spatial position. In terms of ISE, this theorem yields the 
following
fact: Conditioning ISE to put no mass on $]-\infty,-\epsilon[$ and 
letting
$\epsilon$ go to 0 is equivalent to shifting the unconditioned ISE to 
the right
so that the left-most point of its support becomes the origin. We 
derive a
number of explicit estimates and formulas for our conditioned Brownian 
trees.
In particular, the probability that ISE puts no mass on 
$]-\infty,-\epsilon[$
is shown to behave like $2\epsilon^4/21$ when $\epsilon$ goes to 0. 
Finally,
for the conditioned Brownian tree with a fixed height $h$, we obtain a
decomposition involving a spine whose distribution is absolutely 
continuous
with respect to that of a nine-dimensional Bessel process on the time 
interval
$[0,h]$, and Poisson processes of subtrees originating from this spine.


http://front.math.ucdavis.edu/math.PR/0501066

---------------------------------------------------------------

3139. STRONG DISORDER RG APPROACH OF RANDOM SYSTEMS

Ferenc Igloi and Cecile Monthus

There is a large variety of quantum and classical systems in which the
quenched disorder plays a dominant r\^ole over quantum, thermal, or 
stochastic
fluctuations : these systems display strong spatial heterogeneities, 
and many
averaged observables are actually governed by rare regions. A unifying 
approach
to treat the dynamical and/or static singularities of these systems has 
emerged
recently, following the pioneering RG idea by Ma and Dasgupta and the 
detailed
analysis by Fisher who showed that the Ma-Dasgupta RG rules yield 
asymptotic
exact results if the broadness of the disorder grows indefinitely at 
large
scales. Here we report these new developments by starting with an 
introduction
of the main ingredients of the strong disorder RG method. We describe 
the basic
properties of infinite disorder fixed points, which are realized at 
critical
points, and of strong disorder fixed points, which control the singular
behaviors in the Griffiths-phases. We then review in detail 
applications of the
RG method to various disordered models, either (i) quantum models, such 
as
random spin chains, ladders and higher dimensional spin systems, or (ii)
classical models, such as diffusion in a random potential, equilibrium 
at low
temperature and coarsening dynamics of classical random spin chains, 
trap
models, delocalization transition of a random polymer from an 
interface, driven
lattice gases and reaction diffusion models in the presence of quenched
disorder. For several one-dimensional systems, the Ma-Dasgupta RG rules 
yields
very detailed analytical results, whereas for other, mainly higher 
dimensional
problems, the RG rules have to be implemented numerically. If 
available, the
strong disorder RG results are compared with another, exact or numerical
calculations.


http://front.math.ucdavis.edu/cond-mat/0502448

---------------------------------------------------------------

3140. THE EMPIRICAL EIGENVALUE DISTRIBUTION OF A GRAM MATRIX: FROM  
INDEPENDENCE TO STATIONARITY

W. Hachem and  P. Loubaton and J. Najim

Consider a $N\times n$ random matrix $Z_n=(Z^n_{j_1 j_2})$ where the
individual entries are a realization of a properly rescaled stationary 
gaussian
random field.
   The purpose of this article is to study the limiting empirical 
distribution
of the eigenvalues of Gram random matrices such as $Z_n Z_n ^*$ and 
$(Z_n
+A_n)(Z_n +A_n)^*$ where $A_n$ is a deterministic matrix with 
appropriate
assumptions in the case where $n\to \infty$ and $\frac Nn \to c \in
(0,\infty)$.
   The proof relies on related results for matrices with independent but 
not
identically distributed entries and substantially differs from related 
works in
the literature (Boutet de Monvel et al., Girko, etc.).


http://front.math.ucdavis.edu/math.PR/0502535

---------------------------------------------------------------

3141. PRESERVATION OF LOG-CONCAVITY ON SUMMATION

Oliver Johnson and Christina Goldschmidt

We extend Hoggar's result that the sum of two independent 
discrete-valued
log-concave random variables is itself log-concave. Firstly, we weaken 
the
assumption of independence, and introduce conditions under which the 
result
still holds for dependent variables. Secondly, we introduce a wider 
class of
random variables such that in the independent case the sum is still
log-concave, and prove simple results concerning this class.


http://front.math.ucdavis.edu/math.PR/0502548

---------------------------------------------------------------

3142. SEMI-SELFDECOMPOSABLE LAWS AND RELATED PROCESSES

S Satheesh and E Sandhya

In this note we identify Semi-Selfdecomposable Laws as the class of
distributions that can generate a linear, additive, first order 
auto-regressive
scheme, that is marginally stationary. We give a method to construct 
these
distributions. Its implications in selfsimilar and semi-selfsimilar 
processes
with additive increments and their subordination are given. The discrete
analogues of these processes are also discussed.


http://front.math.ucdavis.edu/math.PR/0412546

---------------------------------------------------------------

3143. A NOTE ON RANDOM WALK IN RANDOM SCENERY

Amine Asselah and  Fabienne Castell

We consider a d-dimensional random walk in random scenery X(n), where 
the
scenery consists of i.i.d. with exponential moments but a tail decay of 
the
form exp(-c t^a) with a<d/2. We study the probability, when averaged 
over both
randomness, that {X(n)>ny}. We show that this probability is of order
exp(-(ny)^b) with b=a/(a+1).


http://front.math.ucdavis.edu/math.PR/0501068

---------------------------------------------------------------

3144. PROBABILISTIC AND FRACTAL ASPECTS OF LEVY TREES

Thomas Duquesne (Paris 11) and  Jean-Francois Le Gall (ENS Paris)

We investigate the random continuous trees called L\'evy trees, which 
are
obtained as scaling limits of discrete Galton-Watson trees. We give a
mathematically precise definition of these random trees as random 
variables
taking values in the set of equivalence classes of compact rooted 
R-trees,
which is equipped with the Gromov-Hausdorff distance. To construct 
L\'evy
trees, we make use of the coding by the height process which was 
studied in
detail in previous work. We then investigate various probabilistic 
properties
of L\'evy trees. In particular we establish a branching property 
analogous to
the well-known property for Galton-Watson trees: Conditionally given 
the tree
below level a, the subtrees originating from that level are distributed 
as the
atoms of a Poisson point measure whose intensity involves a local time 
measure
supported on the vertices at distance a from the root. We study 
regularity
properties of local times in the space variable, and prove that the 
support of
local time is the full level set, except for certain exceptional values 
of a
corresponding to local extinctions. We also compute several fractal 
dimensions
of L\'evy trees, including Hausdorff and packing dimensions, in terms 
of lower
and upper indices for the branching mechanism function $\psi$ which
characterizes the distribution of the tree. We finally discuss some
applications to super-Brownian motion with a general branching 
mechanism.


http://front.math.ucdavis.edu/math.PR/0501079

---------------------------------------------------------------

3145. PATH COUPLING USING STOPPING TIMES AND COUNTING INDEPENDENT SETS 
AND  COLOURINGS IN HYPERGRAPHS

Magnus Bordewich and  Martin Dyer and Marek Karpinski

We give a new method for analysing the mixing time of a Markov chain 
using
path coupling with stopping times. We apply this approach to two 
hypergraph
problems. We show that the Glauber dynamics for independent sets in a
hypergraph mixes rapidly as long as the maximum degree Delta of a 
vertex and
the minimum size m of an edge satisfy m>= 2Delta+1. We also show that 
the
Glauber dynamics for proper q-colourings of a hypergraph mixes rapidly 
if m>= 4
and q > Delta, and if m=3 and q>=1.65Delta. We give related results on 
the
hardness of exact and approximate counting for both problems.


http://front.math.ucdavis.edu/math.PR/0501081

---------------------------------------------------------------

3146. RUELLE'S PROBABILITY CASCADES SEEN AS A FRAGMENTATION PROCESS

Anne-Laure Basdevant (LPMA)

In this paper, we study Ruelle's probability cascades in the framework 
of
time-inhomogeneous fragmentation processes. We describe Ruelle's 
cascades
mechanism exhibiting a family of measures $(\nu_t,t\in [0,1[)$ that
characterizes its infinitesimal evolution. To this end, we will first 
extend
the time-homogeneous fragmentation theory to the inhomogeneous case. In 
the
last section, we will study the behavior for small and large times of 
Ruelle's
fragmentation process.


http://front.math.ucdavis.edu/math.PR/0501088

---------------------------------------------------------------

3147. DISCRETE AND CONTINUOUS YANG-MILLS MEASURE FOR NON-TRIVIAL 
BUNDLES OVER  COMPACT SURFACES

Thierry Levy (DMA)

We construct one Yang-Mills measure on a compact surface for each 
isomorphism
class of principal bundles over this surface. For this, we define a new
discrete gauge theory which is essentially a covering of the usual one. 
We
prove that the measures correponding to different isomorphism classes of
bundles or to different total areas of the surface are mutually 
singular. We
give also a combinatorial computation of the partition functions based 
on the
formalism of fat graphs.


http://front.math.ucdavis.edu/math-ph/0501014

---------------------------------------------------------------

3148. THE DIVERGENCE OF FLUCTUATIONS FOR THE SHAPE ON FIRST PASSAGE  
PERCOLATION

Yu Zhang

Consider the first passage percolation model on ${\bf Z}^d$ for $d\geq 
2$. In
this model we assign independently to each edge the value zero with 
probability
$p$ and the value one with probability $1-p$. We denote by $T({\bf 0}, 
v)$ the
passage time from the origin to $v$ for $v\in {\bf R}^d$ and 
$$B(t)=\{v\in {\bf
R}^d: T({\bf 0}, v)\leq t\}{and} G(t)=\{v\in {\bf R}^d: ET({\bf 0}, 
v)\leq
t\}.$$ It is well known that if $p < p_c$, there exists a compact shape
$B_d\subset {\bf R}^d$ such that for all $\epsilon >0$ $$t 
B_d(1-\epsilon)
\subset {B(t)} \subset tB_d(1+\epsilon){and} G(t)(1-{\epsilon}) \subset 
{B(t)}
\subset G(t)(1+{\epsilon}) {eventually w.p.1.}$$ We denote the 
fluctuations of
$B(t)$ from $tB_d$ and $G(t)$ by &&F(B(t), tB_d)=\inf \{l:tB_d(1-{l\over
t})\subset B(t)\subset tB_d(1+{l\over t})\} && F(B(t),
G(t))=\inf\{l:G(t)(1-{l\over t})\subset B(t)\subset G(t)(1+{l\over 
t})\}.
   The means of the fluctuations $E[F(B(t), tB_d]$ and $E[F(B(t), 
G(t))]$ have
been conjectured ranging from divergence to non-divergence for large 
$d\geq 2$
by physicists. In this paper, we show that for all $d\geq 2$ with a high
probability, the fluctuations $F(B(t), G(t))$ and $F(B(t), tB_d)$ 
diverge with
a rate of at least $C \log t$ for some constant $C$.
   The proof of this argument depends on the linearity between the 
number of
pivotal edges of all minimizing paths and the paths themselves. This 
linearity
is also independently interesting.


http://front.math.ucdavis.edu/math.PR/0501095

---------------------------------------------------------------

3149. A RANDOM MATRIX APPROACH TO THE LACK OF PROJECTIONS IN C*_RED(F_2)

Uffe Haagerup and  Hanne Schultz and Steen Thorbjornsen

In 1982 Pimsner and Voiculescu computed the K_0- and K_1-groups of the
reduced group C*-algebra C*_red(F_k) of the free group F_k on k 
generators and
settled thereby a long standing conjecture: C*_red(F_k) has no 
projections
except for the trivial projections 0 and 1. Later simpler proofs of this
conjecture were found by methods from K-theory or from non-commutative
differential geometry. In this paper we provide a new proof of the fact 
that
C*_red(F_k) is projectionless. The new proof is based on random 
matrices and is
obtained by a refinement of the methods recently used by the first and 
the
third named author to show that the semigroup Ext(C*_red(F_k)) is not a 
group
for k >= 2. By the same type of methods we also obtain that two 
phenomena
proved by Bai and Silverstein for certain classes of random matrices: 
``no
eigenvalues outside (a small neighbourhood of) the support of the 
limiting
distribution'' and ``exact separation of eigenvalues by gaps in the 
limiting
distribution'' also hold for arbitrary non-commutative selfadjoint 
polynomials
of independent GUE, GOE or GSE random matrices with matrix coefficients.


http://front.math.ucdavis.edu/math.OA/0412545

---------------------------------------------------------------

3150. TRANSITION FROM THE ANNEALED TO THE QUENCHED ASYMPTOTICS FOR A 
RANDOM  WALK ON RANDOM OBSTACLES

G. Ben Arous and  S. Molchanov and A.F. Ramirez

In this work we study a natural transition mechanism describing the 
passage
from a quenched (almost sure) regime to an annealed (in average) one, 
for a
symmetric simple random walk on random obstacles on sites having an 
identical
and independent law. The transition mechanism we study was first 
proposed in
the context of sums of identical independent random exponents by Ben 
Arous,
Bogachev and Molchanov in \cite{bbm}. Let $p(x,t)$ be the survival 
probability
at time $t$ of the random walk, starting from site $x$, and $L(t)$ be 
some
increasing function of time. We show that the empirical average of 
$p(x,t)$
over a box of side $L(t)$ has different asymptotic behaviors depending 
on
$L(t)$. There are constants $0<\gamma_1<\gamma_2$ such that if $ L(t)\ge
e^{\gamma t^{d/(d+2)}}$, with $\gamma>\gamma_1$, a law of large numbers 
is
satisfied and the empirical survival probability decreases like the 
annealed
one; if $ L(t)\ge e^{\gamma t^{d/(d+2)}}$, with $\gamma>\gamma_2$, also 
a
central limit theorem is satisfied. If $L(t)\ll t$, the averaged 
survival
probability decreases like the quenched survival probability. If $t\ll 
L(t)$
and $\log L(t)\ll t^{d/(d+2)}$ we obtain an intermediate regime. 
Furthermore,
when the dimension $d=1$ it is possible to describe the fluctuations of 
the
averaged survival probability when $L(t)=e^{\gamma t^{d/(d+2)}}$ with
$\gamma<\gamma_2$: it is shown that they are infinitely divisible laws 
with a
L\'evy spectral function which explodes when $x\to 0$ as stable laws of
characteristic exponent $\alpha<2$. These results show that the 
quenched and
annealed survival probabilities correspond to a low and high temperature
behavior of a mean field type phase transition mechanism.


http://front.math.ucdavis.edu/math.PR/0501107

---------------------------------------------------------------

3151. PINNING BY A SPARSE POTENTIAL

Elise Janvresse (LMRS) and  Thierry De La Rue (LMRS) and  Yvan Velenik 
(LMRS)

We consider a directed polymer interacting with a diluted pinning 
potential
restricted to a line. We characterize explicitely the set of disorder
configurations that give rise to localization of the polymer. We study 
both
relevant cases of dimension 1+1 and 1+2. We also discuss the case of 
massless
effective interface models in dimension 2+1.


http://front.math.ucdavis.edu/math.PR/0501135

---------------------------------------------------------------

3152. EDGE-REINFORCED RANDOM WALK ON A LADDER

Franz Merkl and  Silke Rolles

We prove that the edge-reinforced random walk on the ladder Z x {1,2} 
with
initial weights a > 3/4 is recurrent. The proof uses a known 
representation of
the edge-reinforced random walk on a finite piece of the ladder as a 
random
walk in a random environment. This environment is given by a marginal 
of a
multi-component Gibbsian process. A transfer operator technique and 
entropy
estimates from statistical mechanics are used to analyse this Gibbsian 
process.
Furthermore, we prove spatially exponentially fast decreasing bounds for
normalized local times of the edge-reinforced random walk on a finite 
piece of
the ladder, uniformly in the size of the finite piece.


http://front.math.ucdavis.edu/math.PR/0501137

---------------------------------------------------------------

3153. CONVERGENCE OF COALESCING NONSIMPLE RANDOM WALKS TO THE BROWNIAN 
WEB

Rongfeng Sun

The Brownian Web (BW) is a family of coalescing Brownian motions 
starting
from every point in space and time $\R\times\R$. It was first 
introduced by
Arratia, and later analyzed in detail by T\'{o}th and Werner. More 
recently,
Fontes, Isopi, Newman and Ravishankar gave a characterization of the 
BW, and
general convergence criteria allowing either crossing or noncrossing 
paths,
which they verified for coalescing simple random walks. Later Ferrari, 
Fontes,
and Wu verified these criteria for a two dimensional Poisson Tree. In 
both
cases, the paths are noncrossing. In this thesis, we formulate new 
convergence
criteria for crossing paths, and verify them for non-simple coalescing 
random
walks (both discrete and continuous time) satisfying a finite fifth 
moment
condition. This is the first time convergence to the BW has been proved 
for
models with crossing paths. Several corollaries are presented, 
including an
analysis of the scaling limit of voter model interfaces that extends a 
result
of Cox and Durrett.


http://front.math.ucdavis.edu/math.PR/0501141

---------------------------------------------------------------

3154. ALTERNATIVES TO THE NEOBAYESIAN THEOREM, AVOIDING SEVERAL OF ITS  
INCONSISTENCIES: THE RMPE-METHOD

Rainer Gottlob

Some drawbacks of the formalism of Bayes Theorem can be avoided by the
rMPE-Method, a modification of the cMPE-Method that permits (i): Adding
probabilities in spite of non-linearity. (ii): Taking into account 
extensional
evidence and weight-bearing evidence that are mutually dependent, but 
opposed
in their effects. (iii): Arriving at higher probabilities than by Bayes 
Theorem
and (iv): Confirming also hypotheses that imply certain evidence.


http://front.math.ucdavis.edu/math.ST/0501134

---------------------------------------------------------------

3155. THE ISING-SHERRINGTON-KIRPATRICK MODEL IN A MAGNETIC FIELD AT 
HIGH  TEMPERATURE

Francis Comets (PMA) and  Francesco Guerra (Fisica and  Roma 1) and  
Fabio Lucio  Toninelli (Phys-ENS)

We study a spin system on a large box with both Ising interaction and
Sherrington-Kirpatrick couplings, in the presence of an external field. 
Our
results are: (i) existence of the pressure in the limit of an infinite 
box.
When both Ising and Sherrington-Kirpatrick temperatures are high 
enough, we
prove that: (ii) the value of the pressure is given by a suitable 
replica
symmetric solution, and (iii) the fluctuations of the pressure are of 
order of
the inverse of the square of the volume with a normal distribution in 
the
limit. In this regime, the pressure can be expressed in terms of random 
field
Ising models.


http://front.math.ucdavis.edu/math.PR/0501164

---------------------------------------------------------------

3156. TANAKA FORMULA FOR SYMMETRIC L\'{E}VY PROCESSES

Paavo Salminen and  Marc Yor (PMA)

Starting from the potential theoretic definition of the local times of a
Markov process - when these exist - we obtain a Tanaka formula for the 
local
times of symmetric L\'{e}vy processes. The most interesting case is 
that of the
symmetric $\al$-stable L\'{e}vy process (for $\al\in[1,2]$) which is 
studied in
detail. In particular, we determine which powers of such a process are
semimartingales. These results complete, in a sense, the works by K. 
Yamada
\cite{yamada02} and Fitzsimmons and Getoor \cite{fitzsimmonsgetoor92a}.


http://front.math.ucdavis.edu/math.PR/0501182

---------------------------------------------------------------

3157. PARTLY DIVISIBLE PROBABILITY DISTRIBUTIONS

S. Albeverio and  H. Gottschalk and J.-L. Wu

Given a probability distribution $\mu$ a set $\Lambda (\mu)$ of 
positive real
numbers is introduced, so that $\Lambda (\mu)$ measures the 
"divisibility" of
$\mu$. The basic properties of $\Lambda (\mu)$ are described and 
examples of
probability distributions are given, which exhibit the existence of a 
continuum
of situations interpolating the extreme cases of infinitely and 
minimally
divisible probability distributions.


http://front.math.ucdavis.edu/math.PR/0501183

---------------------------------------------------------------

3158. PARTLY DIVISIBLE PROBABILITY MEASURES ON LOCALLY COMPACT ABELIAN 
GROUPS

S. Albeverio and  H. Gottschalk and J.-L. Wu

A notion of admissible probability measures $\mu$ on a locally compact
Abelian group (LCA-group) $G$ with connected dual group $\hat 
G=\R^d\times
\T^n$ is defined. To such a measure $\mu$, a closed semigroup
$\Lambda(\mu)\subseteq (0,\infty)$ can be associated, such that, for 
$t\in
\Lambda(\mu)$, the Fourier transform to the power $t$, $(\hat \mu)^t$, 
is a
characteristic function. We prove that the existence of roots for non
admissible probability measures underlies some restrictions, which do 
not hold
in the admissible case. As we show for the example $\Z_2$, in the case 
of
LCA-groups with non connected dual group, there is no canonical 
definition of
the set $\Lambda(\mu)$.


http://front.math.ucdavis.edu/math.PR/0501185

---------------------------------------------------------------

3159. ESTIMATES OF RANDOM WALK EXIT PROBABILITIES AND APPLICATION TO  
LOOP-ERASED RANDOM WALK

Michael J. Kozdron (University of Regina) and Gregory F. Lawler  
(Cornell University)

We prove an estimate for the probability that a simple random walk in a
simply connected subset A of Z^2 starting on the boundary exits A at 
another
specified boundary point. The estimates are uniform over all domains of 
a given
inradius. We apply these estimates to prove a conjecture of S. Fomin in 
2001
concerning a relationship between crossing probabilities of loop-erased 
random
walk and Brownian motion.


http://front.math.ucdavis.edu/math.PR/0501189

---------------------------------------------------------------

3160. PERCOLATION WITH MULTIPLE GIANT CLUSTERS

E. Ben-Naim and  P.L. Krapivsky

We study the evolution of percolation with freezing. Specifically, we
consider cluster formation via two competing processes: irreversible
aggregation and freezing. We find that when the freezing rate exceeds a 
certain
threshold, the percolation transition is suppressed. Below this 
threshold, the
system undergoes a series of percolation transitions with multiple giant
clusters ("gels") formed. Giant clusters are not self-averaging as 
their total
number and their sizes fluctuate from realization to realization. The 
size
distribution F_k, of frozen clusters of size k, has a universal tail, 
F_k ~
k^{-3}. We propose freezing as a practical mechanism for controlling 
the gel
size.


http://front.math.ucdavis.edu/cond-mat/0501218

---------------------------------------------------------------

3161. GOOD ROUGH PATH SEQUENCES AND APPLICATIONS TO ANTICIPATING & 
FRACTIONAL  STOCHASTIC CALCULUS

Laure Coutin and  Peter Friz and  Nicolas Victoir

We consider anticipative Stratonovich stochastic differential equations
driven by some stochastic process (not necessarily a semi-martingale). 
No
adaptedness of initial point or vector fields is assumed. Under a simple
condition on the stochastic process, we show that the unique solution 
of the
above SDE understood in the rough path sense is actually a Stratonovich
solution. This condition is satisfied by the Brownian motion and the 
fractional
Brownian motion with Hurst parameter greater than 1/4. As application, 
we
obtain rather flexible results such as support theorems, large deviation
principles and Wong-Zakai approximations for SDEs driven by fractional 
Brownian
Motion along anticipating vectorfields. In particular, this unifies many
results on anticipative SDEs.


http://front.math.ucdavis.edu/math.PR/0501197

---------------------------------------------------------------

3162. ON THE INCREMENTS OF THE PRINCIPAL VALUE OF BROWNIAN LOCAL TIME

Endre Cs\'aki and  Yueyun Hu

Let $W$ be a one-dimensional Brownian motion starting from 0. Define 
$Y(t)=
\int_0^t{\d s \over W(s)} := \lim_{\epsilon\to0} \int_0^t 1_{(|W(s)|>
\epsilon)} {\d s \over W(s)} $ as Cauchy's principal value related to 
local
time. We prove limsup and liminf results for the increments of $Y$.


http://front.math.ucdavis.edu/math.PR/0501199

---------------------------------------------------------------

3163. NONINTERSECTING PATHS, NONCOLLIDING DIFFUSION PROCESSES AND  
REPRESENTATION THEORY

Makoto Katori and  Hideki Tanemura

The system of one-dimensional symmetric simple random walks, in which 
none of
walkers have met others in a given time period, is called the vicious 
walker
model. It was introduced by Michael Fisher and applications of the 
model to
various wetting and melting phenomena were described in his Boltzmann 
medal
lecture. In the present report, we explain interesting connections among
representation theory, probability theory, and random matrix theory 
using this
simple diffusion particle system. Each vicious walk of $N$ walkers is
represented by an $N$-tuple of nonintersecting lattice paths on the
spatio-temporal plane. There is established a simple bijection between
nonintersecting lattice paths and semistandard Young tableaux. Based on 
this
bijection and some knowledge of symmetric polynomials called the Schur
functions, we can give a determinantal expression to the partition 
function of
vicious walks, which is regarded as a special case of the 
Karlin-McGregor
formula in the probability theory (or the Lindstr\"om-Gessel-Viennot 
formula in
the enumerative combinatorics). Due to a basic property of Schur 
function, we
can take the diffusion scaling limit of the vicious walks and define a
noncolliding system of Brownian particles. This diffusion process 
solves the
stochastic differential equations with the drift terms acting as the 
repulsive
two-body forces proportional to the inverse of distances between 
particles, and
thus it is identified with Dyson's Brownian motion model. In other 
words, the
obtained noncolliding system of Brownian particles is equivalent in
distribution with the eigenvalue process of a Hermitian matrix-valued 
process.


http://front.math.ucdavis.edu/math.PR/0501218

---------------------------------------------------------------

3164. RANDOM DYNAMICS AND THERMODYNAMIC LIMITS FOR POLYGONAL MARKOV 
FIELDS IN  THE PLANE

Tomasz Schreiber

We construct random dynamics on collections of non-intersecting planar
contours, leaving invariant the distributions of length- and 
area-interacting
polygonal Markov fields with V-shaped nodes. The first of these 
dynamics is
based on the dynamic construction of consistent polygonal fields, as 
presented
in the original articles by Arak (1982) and Arak and Surgailis (1989, 
1991),
and it provides an easy-to-implement Metropolis-type simulation 
algorithm. The
second dynamics leads to a graphical construction in the spirit of 
Fernandez,
Ferrari and Garcia (1998,2002) and it yields a perfect simulation 
scheme in a
finite window from the infinite-volume limit. This algorithm seems 
difficult to
implement, yet its value lies in that it allows for theoretical 
analysis of
thermodynamic limit behaviour of length-interacting polygonal fields. 
The
results thus obtained include the uniqueness and exponential 
$\alpha$-mixing of
the thermodynamic limit of such fields in the low temperature region, 
in the
class of infinite-volume Gibbs measures without infinite contours. 
Outside this
class we conjecture the existence of an infinite number of extreme 
phases
breaking both the translational and rotational symmetries


http://front.math.ucdavis.edu/math.PR/0501228

---------------------------------------------------------------

3165. RANDOM GEOMETRIC GRAPH DIAMETER IN THE UNIT BALL

Robert B. Ellis and  Jeremy L. Martin and  and Catherine Yan

The unit ball random geometric graph $G=G^d_p(\lambda,n)$ has as its 
vertices
$n$ points distributed independently and uniformly in the 
$d$-dimensional unit
ball, with two vertices adjacent if and only if their $l_p$-distance is 
at most
$\lambda$. Like its cousin the Erdos-Renyi random graph, $G$ has a 
connectivity
threshold: an asymptotic value for $\lambda$ in terms of $n$, above 
which $G$
is connected and below which $G$ is disconnected (and in fact has 
isolated
vertices in most cases). In the disconnected zone, we discuss the 
number of
isolated vertices. In the connected zone, we determine upper and lower 
bounds
for the graph diameter of $G$. We employ a combination of methods from
probabilistic combinatorics and stochastic geometry.


http://front.math.ucdavis.edu/math.CO/0501214

---------------------------------------------------------------

3166. STATISTICAL PROPERTIES OF THE PHASE TRANSITIONS IN A SPIN MODEL 
FOR  MARKET MICROSTRUCTURE

Muffasir Badshah and  Robert Boyer and Ted Theodosopoulos

Increased day-trading activity and the subsequent jump in intraday 
volatility
and trading volume fluctuations has raised considerable interest in 
models for
financial market microstructure. We investigate the random transitions 
between
two phases of an agent-based spin market model on a random network. The
objective of the agents is to balance their desire to belong to the 
global
minority and simultaneously to the local majority. We show that 
transitions
between the "ordered" and "disordered" phases follow a Poisson process 
with a
rate that is a monotonically decreasing function of the network 
connectivity.


http://front.math.ucdavis.edu/math.PR/0501244

---------------------------------------------------------------

3167. PROPERTIES OF A RENEWAL PROCESS APPROXIMATION FOR A SPIN MARKET 
MODEL

Muffasir Badshah and  Robert Boyer and Ted Theodosopoulos

In this short note we investigate the natur of the phase transitions in 
a
spin market model as a function of the interaction strength between 
local and
global effects. We find that the stochastic dynamics of this stylized 
market
model exhibit a periodicity whose dependence on the coupling constant 
in the
Ising-like Hamiltonian is robust to changes in the temperature and the 
size of
the market.


http://front.math.ucdavis.edu/math.PR/0501248

---------------------------------------------------------------

3168. FREE TRANSPORTATION COST INEQUALITIES FOR NON-COMMUTATIVE  
MULTI-VARIABLES

Fumio Hiai and Yoshimichi Ueda

We prove the free analogue of the transportation cost inequality for 
tracial
distributions of non-commutative self-adjoint (also unitary) 
multi-variables
based on random matrix approximation procedure.


http://front.math.ucdavis.edu/math.OA/0501238

---------------------------------------------------------------

3169. MULTIDIMENSIONAL BERMUDAN OPTION PRICING VIA CUBATURE AND HOW TO  
EXTRAPOLATE TO PRICE AMERICAN OPTIONS

Frederik S Herzberg

Non-perpetual American option prices shall be approximated by 
non-perpetual
Bermudan option prices, which in turn can be computed in a recombining 
tree of
European options. It will be proven that perpetual and non-perpetual 
Bermudan
option prices have comparable analytic behaviour when perceived as 
functions of
the exercise mesh size. Using a Wiener-Hopf factorisation, a theoretical
formula for perpetual Bermudan option prices is derived. Based on this 
formula,
some rather elementary semigroup analysis gives rise to a power series 
for the
perpetual Bermudan price as a function of the exercise mesh size, 
paving the
way to understand the limiting behaviour as the exercise mesh size 
tends to
naught. Results by Feller that are based on Fourier analytic 
deliberations will
enable us -- for a number of models, including the Black-Scholes and 
Merton's
jump-diffusion models, -- to prove order estimates on the behaviour of 
Bermudan
option prices on stocks with a start price at the exercise boundary. As 
a
consequence, one obtains a natural scaling for the computation of 
American
option prices by means of a non-polynomial extrapolation of Bermudan 
prices.


http://front.math.ucdavis.edu/math.PR/0501261

---------------------------------------------------------------

3170. BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS ON MANIFOLDS

Fabrice Blache

The problem of finding a martingale on a manifold with a fixed random
terminal value can be solved by considering BSDEs with a generator with
quadratic growth. We study here a generalization of these equations and 
we give
uniqueness and existence results in two different frameworks, using
differential geometry tools. Applications to PDEs are given, including a
certain class of Dirichlet problems on manifolds.


http://front.math.ucdavis.edu/math.PR/0501265

---------------------------------------------------------------

3171. SMALL BALL PROBABILITY ESTIMATES IN TERMS OF WIDTH

Rafa{\l} Lata{\l}a and  Krzysztof Oleszkiewicz

A certain inequality conjectured by Vershynin is studied. It is proved 
that
for any $n$-dimensional symmetric convex body $K$ with inradius $w$ and
$\gamma_{n}(K) \leq 1/2$ there is $\gamma_{n}(sK) \leq
(2s)^{w^{2}/4}\gamma_{n}(K)$ for any $s \in [0,1]$. Some natural 
corollaries
are deduced. Another conjecture of Vershynin is proved to be false.


http://front.math.ucdavis.edu/math.PR/0501268

---------------------------------------------------------------

3172. FREE ANALOG OF PRESSURE AND ITS LEGENDRE TRANSFORM

Fumio Hiai

The free analog of the pressure is introduced for multivariate 
noncommutative
random variables and its Legendre transform is compared with 
Voiculescu's
microstate free entropy.


http://front.math.ucdavis.edu/math.OA/0403210

---------------------------------------------------------------

3173. FREE EXTREME VALUES

Gerard Ben Arous and Dan Virgil Voiculescu

Free probability analogues of the basics of extreme value theory are
obtained, based on Ando's spectral order. This includes classification 
of
freely max-stable laws and their domains of attraction, using ``free 
extremal
convolutions'' on the distributions. These laws coincide with the limit 
laws in
the classical peaks-over-threshold approach. A free extremal 
projection-valued
process over a measure-space is constructed, which is related to the 
free
Poisson point process.


http://front.math.ucdavis.edu/math.OA/0501274

---------------------------------------------------------------

3174. POISSON-DIRICHLET DISTRIBUTION FOR RANDOM BELYI SURFACES

A. Gamburd

Brooks and Makover introduced an approach to studying the global 
geometric
quantities (in particular, the first eigenvalue of the Laplacian, 
injectivity
radius and diameter) of a "typical" compact Riemann surface of large 
genus
based on compactifying finite-area Riemann surfaces associated with 
random
cubic graphs; by a theorem of Belyi these are "dense" in the space of 
compact
Riemann surfaces. The question as to how these surfaces are distributed 
in the
Teichm\"{u}ller spaces depends on the study of oriented cycles in 
random cubic
graphs with random orientation; Brooks and Makover conjectured that
asymptotically normalized cycles lengths follow Poisson-Dirichlet 
distribution.
We present a proof of this conjecture using representation theory of the
symmetric group. Consequently we also make progress towards a 
conjecture of
Pippenger and Schleich which arose in the study of topological 
characteristics
of random surfaces generated by cubic interactions.


http://front.math.ucdavis.edu/math.PR/0501283

---------------------------------------------------------------

3175. STATIONARY DISTRIBUTIONS OF MULTI-TYPE TOTALLY ASYMMETRIC 
EXCLUSION  PROCESSES

Pablo A. Ferrari and James B. Martin

We consider totally asymmetric simple exclusion processes with n types 
of
particle and holes (n-TASEPs) on Z and on the cycle Z_N. Angel recently 
gave an
elegant construction of the stationary measures for the 2-TASEP, based 
on a
pair of independent product measures. We show that Angel's construction 
can be
interpreted in terms of the operation of a discrete-time M/M/1 queueing 
server;
the two product measures correspond to the arrival and service 
processes of the
queue. We extend this construction to represent the stationary measures 
of an
n-TASEP in terms of a system of queues in tandem. The proof of 
stationarity
involves a system of n 1-TASEPs, whose evolutions are coupled but whose
distributions at any fixed time are independent. Using the queueing
representation, we give quantitative results for stationary 
probabilities of
states of the n-TASEP on Z_N, and simple proofs of various independence 
and
regeneration properties for systems on Z.


http://front.math.ucdavis.edu/math.PR/0501291

---------------------------------------------------------------

3176. GENERALIZED ARITHMETIC AND GEOMETRIC MEAN DIVERGENCE MEASURE AND 
THEIR  STATISTICAL ASPECTS

Inder Jeet Taneja

Using Blackwell's definition of comparing two experiments, a comparison 
is
made with \textit{generalized AG - divergence} measure having one and 
two
scalar parameters. Connection of \textit{generalized AG - divergence} 
measure
with \textit{Fisher measure of information} is also presented. A unified
\textit{generalization of AG - divergence }and\textit{ Jensen-Shannon
divergence measures} is also presented.


http://front.math.ucdavis.edu/math.PR/0501297

---------------------------------------------------------------

3177. ON MEAN DIVERGENCE MEASURES

Inder Jeet Taneja

\textit{Arithmetic, geometric and harmonic means} are the three 
classical
means famous in the literature. Another mean such as 
\textit{square-root mean}
is also known. In this paper, we have constructed divergence measures 
based on
nonnegative differences among these means, and established an 
interesting
inequality by use of properties of Csisz\'{a}r $f-$\textit{divergence}.
Connections of new \textit{mean divergences} measures with classical 
divergence
measures such as Jeffreys-Kullback-Leiber \cite{jef}, \cite{kul}
\textit{J-divergence}, Sibson-Burbea-Rao \cite{sib}, \cite{bra} 
\textit{Jensen
difference divergence measure} and Taneja \cite{tan2} \textit{AG -- 
divergence}
are also established.


http://front.math.ucdavis.edu/math.PR/0501298

---------------------------------------------------------------

3178. ON UNIFIED GENERALIZATIONS OF RELATIVE JENSEN--SHANNON AND  
ARITHMETIC--GEOMETRIC DIVERGENCE MEASURES, AND THEIR PROPERTIES

Pranesh Kumar and Inder Jeet Taneja

In this paper we shall consider one parametric generalization of some
non-symmetric divergence measures. The \textit{non-symmetric divergence
measures} are such as: Kullback-Leibler \textit{relative information}, 
$\chi
^2-$\textit{divergence}, \textit{relative J -- divergence}, 
\textit{relative
Jensen -- Shannon divergence} and \textit{relative Arithmetic -- 
Geometric
divergence}. All the generalizations considered can be written as 
particular
cases of Csisz\'{a}r's \textit{f-divergence}. By putting some 
conditions on the
probability distribution, the aim here is to develop bounds on these 
measures
and their parametric generalizations.


http://front.math.ucdavis.edu/math.PR/0501299

---------------------------------------------------------------

3179. GENERALIZED NON-SYMMETRIC DIVERGENCE MEASURES AND INEQUALITIES

Inder Jeet Taneja and Pranesh Kumar

In this paper we consider one parameter generalizations of some non -
symmetric divergence measures. Measures are \textit{relative 
information},
$\chi ^2 - $\textit{divergence}, \textit{relative J-divergence},
\textit{relative Jensen-Shannon divergence }and \textit{relative 
arithmetic and
geometric divergence}. All the generalizations considered can be 
written as
particular cases of Csisz\'{a}r \textit{f-divergence}. By conditioning 
the
probability distributions, relationships among the \textit{relative 
divergence
measures }are obtained.


http://front.math.ucdavis.edu/math.PR/0501300

---------------------------------------------------------------

3180. ORNSTEIN-UHLENBECK-CAUCHY PROCESS

Piotr Garbaczewski and Robert Olkiewicz

We combine earlier investigations of linear systems with L\'{e}vy
fluctuations [Physica {\bf 113A}, 203, (1982)] with recent discussions 
of
L\'{e}vy flights in external force fields [Phys.Rev. {\bf E 59},2736, 
(1999)].
We give a complete construction of the Ornstein-Uhlenbeck-Cauchy 
process as a
fully computable model of an anomalous transport and a paradigm example 
of
Doob's stable noise-supported Ornstein-Uhlenbeck process. Despite the
nonexistence of all moments, we determine local characteristics 
(forward drift)
of the process, generators of forward and backward dynamics, relevant
(pseudodifferential) evolution equations. Finally we prove that this 
random
dynamics is not only mixing (hence ergodic) but also exact. The induced
nonstationary spatial process is proved to be Markovian and quite apart 
from
its inherent discontinuity defines an associated velocity process in a
probabilistic sense.


http://front.math.ucdavis.edu/chao-dyn/9910028

---------------------------------------------------------------

3181. BURGERS VELOCITY FIELDS AND DYNAMICAL TRANSPORT PROCESSES

P. Garbaczewski and  G. Kondrat

We explore a connection of the forced Burgers equation with the
Schr\"{o}dinger (diffusive) interpolating dynamics in the presence of
deterministic external forces. This entails an exploration of the 
consistency
conditions that allow to interpret dispersion of passive contaminants 
in the
Burgers flow as a Markovian diffusion process. In general, the usage of 
a
continuity equation $\partial_t\rho =-\nabla (\vec{v}\rho)$, where
$\vec{v}=\vec{v}(\vec{x},t)$ stands for the Burgers field and $\rho $ 
is the
density of transported matter, is at variance with the explicit 
diffusion
scenario. Under these circumstances, we give a complete 
characterisation of the
diffusive matter transport that is governed by Burgers velocity fields. 
The
result extends both to the approximate description of the transport 
driven by
an incompressible fluid and to motions in an infinitely compressible 
medium.


http://front.math.ucdavis.edu/cond-mat/9802060

---------------------------------------------------------------

3182. CAUCHY NOISE AND AFFILIATED STOCHASTIC PROCESSES

P. Garbaczewski and R. Olkiewicz

By departing from the previous attempt (Phys. Rev. {\bf E 51}, 4114, 
(1995))
we give a detailed construction of conditional and perturbed Markov 
processes,
under the assumption that the Cauchy law of probability replaces the 
Gaussian
law (appropriate for the Wiener process) as the model of primordial 
noise. All
considered processes are regarded as probabilistic solutions of the 
so-called
Schr\"{o}dinger interpolation problem, whose validity is thus extended 
to the
jump-type processes and their step process approximants.


http://front.math.ucdavis.edu/math-ph/9804014

---------------------------------------------------------------

3183. THE SCHROEDINGER PROBLEM, LEVY PROCESSES NOISE IN RELATIVISTIC 
QUANTUM  MECHANICS

P. Garbaczewski and  J. R. Klauder and  R. Olkiewicz

The main purpose of the paper is an essentially probabilistic analysis 
of
relativistic quantum mechanics. It is based on the assumption that 
whenever
probability distributions arise, there exists a stochastic process that 
is
either responsible for temporal evolution of a given measure or 
preserves the
measure in the stationary case. Our departure point is the so-called
Schr\"{o}dinger problem of probabilistic evolution, which provides for 
a unique
Markov stochastic interpolation between any given pair of boundary 
probability
densities for a process covering a fixed, finite duration of time, 
provided we
have decided a priori what kind of primordial dynamical semigroup 
transition
mechanism is involved. In the nonrelativistic theory, including quantum
mechanics, Feyman-Kac-like kernels are the building blocks for suitable
transition probability densities of the process. In the standard "free" 
case
(Feynman-Kac potential equal to zero) the familiar Wiener noise is 
recovered.
In the framework of the Schr\"{o}dinger problem, the "free noise" can 
also be
extended to any infinitely divisible probability law, as covered by the
L\'{e}vy-Khintchine formula. Since the relativistic Hamiltonians 
$|\nabla |$
and $\sqrt {-\triangle +m^2}-m$ are known to generate such laws, we 
focus on
them for the analysis of probabilistic phenomena, which are shown to be
associated with the relativistic wave (D'Alembert) and matter-wave
(Klein-Gordon) equations, respectively. We show that such stochastic 
processes
exist and are spatial jump processes. In general, in the presence of 
external
potentials, they do not share the Markov property, except for stationary
situations. A concrete example of the pseudodifferential 
Cauchy-Schr\"{o}dinger
evolution is analyzed in detail. The relativistic covariance of related 
wave


http://front.math.ucdavis.edu/quant-ph/9505003

---------------------------------------------------------------

3184. FEYNMAN-KAC KERNELS IN MARKOVIAN REPRESENTATIONS OF THE 
SCHROEDINGER  INTERPOLATING DYNAMICS

Piotr Garbaczewski and Robert Olkiewicz

Probabilistic solutions of the so called Schr\"{o}dinger boundary data
problem provide for a unique Markovian interpolation between any two 
strictly
positive probability densities designed to form the input-output 
statistics
data for the process taking place in a finite-time interval. The key 
issue is
to select the jointly continuous in all variables positive Feynman-Kac 
kernel,
appropriate for the phenomenological (physical) situation. We extend the
existing formulations of the problem to cases when the kernel is \it 
not \rm a
fundamental solution of a parabolic equation, and prove the existence 
of a
continuous Markov interpolation in this case. Next, we analyze the
compatibility of this stochastic evolution with the original parabolic
dynamics, while assumed to be governed by the temporally adjoint pair of
(parabolic) partial differential equations, and prove that the 
pertinent random
motion is a diffusion process. In particular, in conjunction with Born's
statistical interpretation postulate in quantum theory, we consider 
stochastic
processes which are compatible with the Schr\"{o}dinger picture quantum
evolution.


http://front.math.ucdavis.edu/quant-ph/9505012

---------------------------------------------------------------

3185. INFORMATION THEORY, RELATIVE VERSIONS OF THE HYPERGRAPH 
REGULARITY AND  REMOVAL LEMMAS, THE SZEMER\'EDI-FURSTENBERG-KATZNELSON 
THEOREM, AND PRIME
   CONSTELLATIONS IN NUMBER FIELDS

Terence Tao

We present a proof of the Szemer\'edi-Furstenberg-Katznelson theorem
concerning multidimensional arithmetic progressions, using the Shannon 
entropy
inequalities to establish an information-theoretic analogue of the
Szemer\'edi-Gowers-R\"odl-Skokan hypergraph regularity lemma. In 
particular we
give (yet another) a self-contained proof of Szemer\'edi's famous 
theorem on
arithmetic progressions, as well as the extension to pseudorandom 
measures
obtained recently by Green and the author. As an application, we 
combine these
methods with the Goldston-Y{\i}ld{\i}r{\i}m type analysis in that paper 
to
reprove that the primes contain arbitrarily long arithmetic 
progressions, and
in fact (partially) extend this result to higher dimensions and to 
other number
fields, establishing in particular that there are infinitely many
constellations of primes of a prescribed shape in the Gaussian integers
$\Z[i]$.


http://front.math.ucdavis.edu/math.CO/0501314

---------------------------------------------------------------

3186. PERCOLATION-LIKE SCALING EXPONENTS FOR MINIMAL PATHS AND TREES IN 
THE  STOCHASTIC MEAN FIELD MODEL

David J. Aldous

In the mean field (or random link) model there are $n$ points and 
inter-point
distances are independent random variables. For $0 < \ell < \infty$ and 
in the
$n \to \infty$ limit, let $\delta(\ell) = 1/n \times$ (maximum number 
of steps
in a path whose average step-length is $\leq \ell$). The function
$\delta(\ell)$ is analogous to the percolation function in percolation 
theory:
there is a critical value $\ell_* = e^{-1}$ at which $\delta(\cdot)$ 
becomes
non-zero, and (presumably) a scaling exponent $\beta$ in the sense
$\delta(\ell) \asymp (\ell - \ell_*)^\beta$. Recently developed 
probabilistic
methodology (in some sense a rephrasing of the cavity method of 
Mezard-Parisi)
provides a simple albeit non-rigorous way of writing down such 
functions in
terms of solutions of fixed-point equations for probability 
distributions.
Solving numerically gives convincing evidence that $\beta = 3$. A 
parallel
study with trees instead of paths gives scaling exponent $\beta = 2$. 
The new
exponents coincide with those found in a different context (comparing 
optimal
and near-optimal solutions of mean-field TSP and MST) and reinforce the
suggestion that these scaling exponents determine universality classes 
for
optimization problems on random points.


http://front.math.ucdavis.edu/cond-mat/0501473

---------------------------------------------------------------

3187. GENERALISED SIFTING IN BLACK-BOX GROUPS

Sophie Ambrose and  Max Neunhoeffer and  Cheryl E. Praeger and Csaba 
Schneider

We present a generalisation of the sifting procedure introduced 
originally by
Sims for computation with finite permutation groups, and now used for 
many
computational procedures for groups, such as membership testing and 
finding
group orders. Our procedure is a Monte Carlo algorithm, and is 
presented and
analysed in the context of black-box groups. It is based on a chain of 
subsets
instead of a subgroup chain. Two general versions of the procedure are 
worked
out in detail, and applications are given for membership tests for 
several of
the sporadic simple groups.
   Our major objective was that the procedures could be proved to be 
Monte Carlo
algorithms, and their costs computed. In addition we explicitly 
determined
suitable subset chains for six of the sporadic groups, and we 
implemented the
algorithms involving these chains in the {\sf GAP} computational algebra
system. It turns out that sample implementations perform well in 
practice. The
implementations will be made available publicly in the form of a {\sf 
GAP}
package.


http://front.math.ucdavis.edu/math.GR/0501346

---------------------------------------------------------------

3188. THE STATIONARY MEASURE OF A 2-TYPE TOTALLY ASYMMETRIC EXCLUSION 
PROCESS

Omer Angel

We give a combinatorial description of the stationary measure for a 
totally
asymmetric exclusion process (TASEP) with second class particles, on 
either Z
or on the cycle Z_N. The measure is the image by a simple operation of 
the
uniform measure on some larger finite state space. This reveals a 
combinatorial
structure at work behind several results on the TASEP with second class
particles.


http://front.math.ucdavis.edu/math.PR/0501005

---------------------------------------------------------------

3189. SIGNAL SIGNIFICANCE IN THE PRESENCE OF SYSTEMATIC AND STATISTICAL 
  UNCERTAINTIES

S.I. Bityukov (IHEP and  Protvino)

The incorporation of uncertainties to calculations of signal 
significance in
planned experiments is an actual task. Several approaches to this 
problem are
discussed. We present a procedure for taking into account the systematic
uncertainty related to nonexact knowledge of signal and background cross
sections. A method of a treatment of statistical errors of the expected 
signal
and background rates is proposed. The interrelation between Gamma- and 
Poisson
distributions is demonstrated.


http://front.math.ucdavis.edu/hep-ph/0207130

---------------------------------------------------------------

3190. THE PROBABILITY OF MAKING A CORRECT DECISION IN HYPOTHESES 
TESTING AS  ESTIMATOR OF QUALITY OF PLANNED EXPERIMENTS

S.I. Bityukov (IHEP and  Protvino) and  N.V. Krasnikov (INR RAS and  
Moscow)

In the report the approach to estimation of quality of planned 
experiments is
considered. This approach is based on the analysis of uncertainty, 
which will
take place under the future hypotheses testing about the existence of a 
new
phenomenon in Nature. The probability of making a correct decision in
hypotheses testing is proposed as estimator of quality of planned 
experiments.
This estimator allows to take into account systematics and statistical
uncertainties in determination of signal and background rates.


http://front.math.ucdavis.edu/physics/0309031

---------------------------------------------------------------

3191. A REVERSION OF THE CHERNOFF BOUND

Ted Theodosopoulos

This paper describes the construction of a lower bound for the tails of
general random variables, using solely knowledge of their moment 
generating
function. The tilting procedure used allows for the construction of 
lower
bounds that are tighter and more broadly applicable than existing tail
approximations.


http://front.math.ucdavis.edu/math.PR/0501360

---------------------------------------------------------------

3192. THE OVERHAND SHUFFLE MIXES IN $\THETA(N^2 \LOG N)$ STEPS

Johan Jonasson

The overhand shuffle is one of the ``real'' card shuffling methods in 
the
sense that some people actually use it to mix a deck of cards. A 
mathematical
model was constructed and analyzed by Pemantle [\ref{Pemantle}] who 
showed that
the mixing time with respect to variation distance is at least of order 
$n^2$
and at most of order $n^2\log n$. In this paper we use an extension of 
a lemma
of Wilson [\ref{Wilson}] to establish a lower bound of order $n^2 \log 
n$,
thereby showing that $n^2 \log n$ is indeed the correct order of the 
mixing
time. It is our hope that the extension of Wilson's Lemma will prove 
useful
also in other situations; it is demonstrated how it may be used to give 
a
simplified proof of the $\Theta(n^3\log n)$ lower bound of Wilson
[\ref{Wilson2}] for the Rudvalis shuffle.


http://front.math.ucdavis.edu/math.PR/0501401

---------------------------------------------------------------

3193. DYNAMICALLY CONSISTENT NONLINEAR EVALUATIONS AND EXPECTATIONS

Shi-Ge Peng

How an economic agent (a firm, an investor or a financial market) 
evaluates a
contingent claim, say a European type of derivatives X, with maturity 
t? In
this paper we study a mechanism of dynamic expectations and 
evaluations. We
give the axiomatic conditions of the time consistency. We prove that, 
under a
domination condition, a time consistent nonlinear evaluation is in fact 
a
g-expectation, i.e., it is completely determined a BSDE in which the 
generator
is a given function g.


http://front.math.ucdavis.edu/math.PR/0501415

---------------------------------------------------------------

3194. TAIL-SENSITIVE GAUSSIAN ASYMPTOTICS FOR MARGINALS OF CONCENTRATED 
  MEASURES IN HIGH DIMENSION

Sasha Sodin

If the Euclidean norm is strongly concentrated with respect to a 
measure, the
average distribution of an average marginal of this measure has Gaussian
asymptotics that captures tail behaviour. If the marginals of the 
measure have
exponential moments, Gaussian asymptotics for the distribution of the 
average
marginal implies Gaussian asymptotics for the distribution of most 
individual
marginals. We show applications to measures of geometric origin.


http://front.math.ucdavis.edu/math.MG/0501382

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3195. A FREE ANALOGUE OF THE TRANSPORTATION COST INEQUALITY ON THE 
CIRCLE

F. Hiai and D. Petz

We give a new proof of the free transportation cost inequality for 
measures
on the circle following M. Ledoux's idea.


http://front.math.ucdavis.edu/math.OA/0501389

---------------------------------------------------------------

3196. ALMOST SURE ESTIMATES FOR THE CONCENTRATION NEIGHBORHOOD OF 
SINAI'S WALK

Pierre Andreoletti (LATP)

We consider Sinai's random walk in random environment. We prove that
infinitely often (i.o.) the size of the concentration neighborhood of 
this
random walk is almost surely bounded. As an application we get that 
i.o. the
maximal distance between two favorite sites is almost surely bounded.


http://front.math.ucdavis.edu/math.PR/0501439

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3197. SCALING OF PERCOLATION ON INFINITE PLANAR MAPS, I

Omer Angel

We consider several aspects of the scaling limit of percolation on 
random
planar triangulations, both finite and infinite. The equivalents for 
random
maps of Cardy's formula for the limit under scaling of various crossing
probabilities are given. The limit probabilities are expressed in terms 
of
simple events regarding Airy-Levy processes. Some explicit formulas for 
limit
probabilities follow from this relation by applying known results on 
stable
processes. Conversely, natural symmetries of the random maps imply 
identities
concerning the Airy-Levy processes.


http://front.math.ucdavis.edu/math.PR/0501006

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3198. POSITIVE HARMONIC FUNCTIONS FOR SEMI-ISOTROPIC RANDOM WALKS ON 
TREES,  LAMPLIGHTER GROUPS, AND DL-GRAPHS

Sara Brofferio and  Wolfgang Woess

We determine all positive harmonic functions for a large class of
"semi-isotropic" random walks on the lamplighter group, i.e., the wreath
product of the cyclic group of order q with the infinite cyclic group. 
This is
possible via the geometric realization of a Cayley graph of that group 
as the
Diestel-Leader graph DL(q,q). More generally, DL(q,r) is the horocyclic 
product
of two homogeneous trees with respective degrees $q+1$ and $r+1$, and 
our
result applies to all DL-graphs. This is based on a careful study of the
minimal harmonic functions for semi-isotropic walks on trees.


http://front.math.ucdavis.edu/math.PR/0501440

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3199. AN EQUIVALENT REPRESENTATION OF THE JACOBI FIELD OF A L\'EVY 
PROCESS

Eugene Lytvynov

In [Yu.M. Berezansky, E. Lytvynov, D. A. Mierzejewski, Ukrainian Math. 
J. 55
(2003), 853--858 ], the Jacobi field of a L\'evy process was derived. 
This
field consists of commuting self-adjoint operators acting in an extended
(interacting) Fock space. However, these operators have a quite 
complicated
structure. In this note, using ideas from [L. Accardi. U. Franz, M. 
Skeide,
Comm. Math. Phys. 228 (2002), 123--150] and [E. Lytvynov, Infin. Dimen. 
Anal.
Quant. Prob. Rel. Top. 7 (2004), 619--629], we obtain a unitary 
equivalent
representation of the Jacobi field of a L\'evy process. In this 
representation,
the operators act in a usual symmetric Fock space and have a much 
simpler
structure.


http://front.math.ucdavis.edu/math.PR/0501450

---------------------------------------------------------------

3200. MIN-MAX VARIATIONAL PRINCIPLE AND FRONT SPEEDS IN RANDOM SHEAR 
FLOWS

James Nolen and Jack Xin

Speed ensemble of bistable (combustion) fronts in mean zero stationary
Gaussian shear flows inside two and three dimensional channels is 
studied with
a min-max variational principle. In the small root mean square regime 
of shear
flows, a new class of multi-scale test functions are found to yield 
speed
asymptotics. The quadratic speed enhancement law holds with probability
arbitrarily close to one under the almost sure continuity (dimension 
two) and
mean square H\"older regularity (dimension three) of the shear flows. 
Remarks
are made on the conditions for the linear growth of front speed 
expectation in
the large root mean square regime.


http://front.math.ucdavis.edu/math.AP/0501445

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3201. ON THE CONCENTRATION OF SINAI'S WALK

Pierre Andreoletti (CPT)

We consider Sinai's random walk in random environment. We prove that 
for an
interval of time [1,n] Sinai's walk sojourns in a small neighborhood of 
the
point of localization for the quasi totality of this amount of time. 
Moreover
the local time at the point of localization normalized by $n$ converges 
in
probability to a well defined random variable of the environment.


http://front.math.ucdavis.edu/math.PR/0501466

---------------------------------------------------------------

3202. ALTERNATIVE PROOF FOR THE LOCALIZATION OF SINAI'S WALK

Pierre Andreoletti

We give an alternative proof of the localization of Sinai's random walk 
in
random environment under weaker hypothesis than the ones used by Sinai.
Moreover we give estimates that are stronger than the one of Sinai on 
the
localization neighborhood and on the probability for the random walk to 
stay
inside this neighborhood.


http://front.math.ucdavis.edu/math.PR/0501467

---------------------------------------------------------------

3203. ON THE CONCENTRATION OF SINAI'S WALK

Pierre Andreoletti (CPT)

We consider Sinai's random walk in random environment. We prove that 
for an
interval of time [1,n] Sinai's walk sojourns in a small neighborhood of 
the
point of localization for the quasi totality of this amount of time. 
Moreover
the local time at the point of localization normalized by $n$ converges 
in
probability to a well defined random variable of the environment.


http://front.math.ucdavis.edu/math.PR/0501466

---------------------------------------------------------------

3204. ALTERNATIVE PROOF FOR THE LOCALIZATION OF SINAI'S WALK

Pierre Andreoletti

We give an alternative proof of the localization of Sinai's random walk 
in
random environment under weaker hypothesis than the ones used by Sinai.
Moreover we give estimates that are stronger than the one of Sinai on 
the
localization neighborhood and on the probability for the random walk to 
stay
inside this neighborhood.


http://front.math.ucdavis.edu/math.PR/0501467

From pas at www.economia.unimi.it  Mon May  2 02:13:18 2005
From: pas at www.economia.unimi.it (pas@www.economia.unimi.it)
Date: Mon May  2 17:38:12 2005
Subject: [Pas] Probability Abstract 86
Message-ID: <d9d004d6872693a9c183425b4fcb3702@unimi.it>

                                                                         
                         May 2, 2005
                                                                         
                         Letter 86

Probability Abstract Service



---------------------------------------------------------------

3205. RANDOM GRAPHS WITH ARBITRARY I.I.D. DEGREES

Remco van der Hofstad and  Gerard Hooghiemstra and  Dmitri Znamenski

In this paper we study distances and connectivity properties of random 
graphs
with an arbitrary i.i.d. degree sequence. When the tail of the degree
distribution is regularly varying with exponent $1-\tau$ there are three
distinct cases: (i) $\tau>3$, where the degrees have finite variance, 
(ii)
$\tau\in (2,3)$, where the degrees have infinite variance, but finite 
mean, and
(iii) $\tau\in (1,2)$, where the degrees have infinite mean. These 
random
graphs can serve as models for complex networks where degree power laws 
are
observed. The distances between pairs of nodes in the three cases 
mentioned
above have been studied in three previous publications, and we survey 
the
results obtained there. Apart from the critical cases $\tau=1$, 
$\tau=2$ and
$\tau=3$, this completes the scaling picture. We explain the results
heuristically and describe related work and open problems. We also 
compare the
behavior in this model to Internet data, where a degree power law with 
exponent
$\tau\approx 2.2$ is observed.
   Furthermore, in this paper we derive results concerning the connected
components and the diameter. We give a criterion when there exists a 
unique
largest connected component of size proportional to the size of the 
graph, and
study sizes of the other connected components. Also, we show that for 
$\tau\in
(2,3)$, which is most often observed in real networks, the diameter in 
this
model grows much faster than the typical distance between two arbitrary 
nodes.


http://front.math.ucdavis.edu/math.PR/0502580

---------------------------------------------------------------

3206. THE SINGLE SERVER QUEUE AND THE STORAGE MODEL: LARGE DEVIATIONS 
AND  FIXED POINTS

Moez Draief

We consider the coupling of a single server queue and a storage model 
defined
as a Queue/Store model in Draief et al. 2004. We establish that if the 
input
variables both arrivals to the queue and to the store satisfy large 
deviations
principles and are linked through an {\em exponential tilting} than the 
output
variables (departures from each system) satisfy large deviations 
principles
with the same rate function. This generalizes to the context of large
deviations the extension of Burke's Theorem derived in Draief et al. 
2004.


http://front.math.ucdavis.edu/math.PR/0503016

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3207. SUBEXPONENTIAL ASYMPTOTICS OF HYBRID FLUID AND RUIN MODELS

Bert Zwart and  Sem Borst and Krzystof Debicki

We investigate the tail asymptotics of the supremum of X(t)+Y(t)-ct, 
where
X={X(t),t\geq 0} and Y={Y(t),t\geq 0} are two independent stochastic 
processes.
We assume that the process Y has subexponential characteristics and 
that the
process X is more regular in a certain sense than Y. A key issue 
examined in
earlier studies is under what conditions the process X contributes to 
large
values of the supremum only through its average behavior. The present 
paper
studies various scenarios where the latter is not the case, and the 
process X
shows some form of ``atypical'' behavior as well. In particular, we 
consider a
fluid model fed by a Gaussian process X and an (integrated) On-Off 
process Y.
We show that, depending on the model parameters, the Gaussian process 
may
contribute to the tail asymptotics by its moderate deviations, large
deviations, or oscillatory behavior.


http://front.math.ucdavis.edu/math.PR/0503482

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3208. DEVIATION INEQUALITIES VIA COUPLING FOR STOCHASTIC PROCESSES AND 
RANDOM  FIELDS

J.-R. Chazottes and  P. Collet and  C. Kuelske and  F. Redig

We present a new and simple approach to deviation inequalities for
non-product measures, i.e., for dependent random variables. Our method 
is based
on coupling. We illustrate our abstract results with chains with 
complete
connections and Gibbsian random fields, both at high and low 
temperature.


http://front.math.ucdavis.edu/math.PR/0503483

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3209. AN APPROXIMATE SAMPLING FORMULA UNDER GENETIC HITCHHIKING

A. M. Etheridge and  P. Pfaffelhuber and A. Wakolbinger

For a genetic locus carrying a strongly beneficial allele which has just
fixed in a large population we study the ancestry at a linked neutral 
locus.
During this ''selective sweep'' the linkage between the two loci is 
broken up
by recombination, and the ancestry at the neutral locus is modelled by a
structured coalescent in a random background. For large selection 
coefficients
$\alpha$ and under an appropriate scaling of the recombination rate, we 
derive
a sampling formula with an order of accuracy of $O((\log\alpha)^{-2})$ 
in
probability. In particular we see that, with this order of accuracy, in 
a
sample of fixed size there are at most two non-singleton families of
individuals which are identi cal by descent at the neutral locus from 
the
beginning of the sweep. This refines a formula going back to the work of
Maynard Smith and Haigh, and co mplements recent work of Schweinsberg 
and
Durrett on selective sweeps in the Moran model.


http://front.math.ucdavis.edu/math.PR/0503485

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3210. LARGE DEVIATIONS OF A MODIFIED JACKSON NETWORK: STABILITY AND 
ROUGH  ASYMPTOTICS

Robert D. Foley and David R. McDonald

Consider a modified, stable, two node Jackson network where server 2 
helps
server 1 when server 2 is idle. The probability of a large deviation of 
the
number of customers at node one can be calculated using the flat 
boundary
theory of Schwartz and Weiss [Large Deviations Performance Analysis 
(1994),
  Chapman and Hall, New York]. Surprisingly, however, these calculations 
show
that the proportion of time spent on the boundary, where server 2 is 
idle, may
be zero. This is in sharp contrast to the unmodified Jackson network 
which
spends a nonzero proportion of time on this boundary.


http://front.math.ucdavis.edu/math.PR/0503487

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3211. BRIDGES AND NETWORKS: EXACT ASYMPTOTICS

Robert D. Foley and David R. McDonald

We extend the Markov additive methodology developed in [Ann. Appl. 
Probab. 9
(1999) 110-145, Ann. Appl. Probab. 11 (2001) 596-607] to obtain the 
sharp
asymptotics of the steady state probability of a queueing network when 
one of
the nodes gets large. We focus on a new phenomenon we call a bridge. 
The bridge
cases occur when the Markovian part of the twisted Markov additive 
process is
one null recurrent or one transient, while the jitter cases treated in 
[Ann.
Appl. Probab. 9 (1999) 110-145, Ann. Appl. Probab. 11 (2001) 596-607] 
occur
when the Markovian part is (one) positive recurrent. The asymptotics of 
the
steady state is an exponential times a polynomial term in the bridge 
case, but
is purely exponential in the jitter case. We apply this theory to a 
modified,
stable, two node Jackson network where server two helps server one when 
server
two is idle. We derive the sharp asymptotics of the steady state 
distribution
of the number of customers queued at each node as the number of 
customers
queued at the server one grows large. In so doing we get an intuitive
understanding of the companion paper [Ann. Appl. Probab. 15 (2005) 
519-541]
which gives a large deviation analysis of this problem using the flat 
boundary
theory in the book by Shwartz and Weiss. Unlike the (unscaled) large 
deviation
path of a Jackson network which jitters along the boundary, the 
unscaled large
deviation path of the modified network tries to avoid the boundary 
where server
two helps server one (and forms a bridge).


http://front.math.ucdavis.edu/math.PR/0503488

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3212. UPPER BOUNDS FOR SPATIAL POINT PROCESS APPROXIMATIONS

Dominic Schuhmacher

We consider the behavior of spatial point processes when subjected to a 
class
of linear transformations indexed by a variable T. It was shown in 
Ellis [Adv.
in Appl. Probab. 18 (1986) 646-659] that, under mild assumptions, the
transformed processes behave approximately like Poisson processes for 
large T.
In this article, under very similar assumptions, explicit upper bounds 
are
given for the d_2-distance between the corresponding point process
distributions. A number of related results, and applications to kernel 
density
estimation and long range dependence testing are also presented. The 
main
results are proved by applying a generalized Stein-Chen method to 
discretized
versions of the point processes.


http://front.math.ucdavis.edu/math.PR/0503491

---------------------------------------------------------------

3213. NOISE STABILITY OF FUNCTIONS WITH LOW INFLUENCES: INVARIANCE AND  
OPTIMALITY

Elchanan Mossel and Ryan O'Donnell and Krzysztof Oleszkiewicz

In this paper we study functions with low influences on product 
probability
spaces. The analysis of boolean functions with low influences has 
become a
central problem in discrete Fourier analysis. It is motivated by 
fundamental
questions arising from the construction of probabilistically checkable 
proofs
in theoretical computer science and from problems in the theory of 
social
choice in economics.
   We prove an invariance principle for multilinear polynomials with low
influences and bounded degree; it shows that under mild conditions the
distribution of such polynomials is essentially invariant for all 
product
spaces. Ours is one of the very few known non-linear invariance 
principles. It
has the advantage that its proof is simple and that the error bounds are
explicit. We also show that the assumption of bounded degree can be 
eliminated
if the polynomials are slightly ``smoothed''; this extension is 
essential for
our applications to ``noise stability''-type problems.
   In particular, as applications of the invariance principle we prove 
two
conjectures: the ``Majority Is Stablest'' conjecture from theoretical 
computer
science, which was the original motivation for this work, and the ``It 
Ain't
Over Till It's Over'' conjecture from social choice theory.


http://front.math.ucdavis.edu/math.PR/0503503

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3214. LOGARITHMIC SOBOLEV INEQUALITY FOR LOG-CONCAVE MEASURE FROM  
PREKOPA-LEINDLER INEQUALITY

Ivan Gentil

We develop in this paper an amelioration of the method given by S. 
Bobkov and
M. Ledoux in GAFA (2000). We prove by Prekopa-Leindler Theorem an 
optimal
modified logarithmic Sobolev inequality adapted for all log-concave 
measure on
$\dR^n$. This inequality implies results proved by Bobkov and Ledoux, 
the
Euclidean Logarithmic Sobolev inequality generalized in the last years 
and it
also implies some convex logarithmic Sobolev inequalities for large 
entropy.


http://front.math.ucdavis.edu/math.FA/0503476

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3215. EQUILIBRIUM GLAUBER AND KAWASAKI DYNAMICS OF CONTINUOUS PARTICLE 
SYSTEMS

Yu. G. Kondratiev and  E. Lytvynov and  M. R\"ockner

We construct two types of equilibrium dynamics of infinite particle 
systems
in a Riemannian manifold $X$. These dynamics are analogs of the Glauber,
respectively Kawasaki dynamics of lattice spin systems. The Glauber 
dynamics
now is a process where interacting particles randomly appear and 
disappear,
i.e., it is a birth-and-death process in $X$, while in the Kawasaki 
dynamics
interacting particles randomly jump over $X$. We establish conditions 
on a
priori explicitly given symmetrizing measures and generators of both 
dynamics
under which corresponding conservative Markov processes exist.


http://front.math.ucdavis.edu/math.PR/0503042

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3216. THE STEPPING STONE MODEL. II: GENEALOGIES AND THE INFINITE SITES 
MODEL

Iljana Zahle and  J. Theodore Cox and Richard Durrett

This paper extends earlier work by Cox and Durrett, who studied the
coalescence times for two lineages in the stepping stone model on the
two-dimensional torus. We show that the genealogy of a sample of size n 
is
given by a time change of Kingman's coalescent. With DNA sequence data 
in mind,
we investigate mutation patterns under the infinite sites model, which 
assumes
that each mutation occurs at a new site. Our results suggest that the 
spatial
structure of the human population contributes to the haplotype 
structure and a
slower than expected decay of genetic correlation with distance 
revealed by
recent studies of the human genome.


http://front.math.ucdavis.edu/math.PR/0503512

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3217. RENEWAL THEORY AND COMPUTABLE CONVERGENCE RATES FOR GEOMETRICALLY 
  ERGODIC MARKOV CHAINS

Peter H. Baxendale

We give computable bounds on the rate of convergence of the transition
probabilities to the stationary distribution for a certain class of
geometrically ergodic Markov chains. Our results are different from 
earlier
estimates of Meyn and Tweedie, and from estimates using coupling, 
although we
start from essentially the same assumptions of a drift condition toward 
a
``small set.'' The estimates show a noticeable improvement on existing 
results
if the Markov chain is reversible with respect to its stationary 
distribution,
and especially so if the chain is also positive. The method of proof 
uses the
first-entrance-last-exit decomposition, together with new quantitative 
versions
of a result of Kendall from discrete renewal theory.


http://front.math.ucdavis.edu/math.PR/0503515

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3218. UTILITY MAXIMIZATION WITH A STOCHASTIC CLOCK AND AN UNBOUNDED 
RANDOM  ENDOWMENT

Gordan Zitkovic

We introduce a linear space of finitely additive measures to treat the
problem of optimal expected utility from consumption under a stochastic 
clock
and an unbounded random endowment process. In this way we establish 
existence
and uniqueness for a large class of utility-maximization problems 
including the
classical ones of terminal wealth or consumption, as well as the 
problems that
depend on a random time horizon or multiple consumption instances. As an
example we explicitly treat the problem of maximizing the logarithmic 
utility
of a consumption stream, where the local time of an Ornstein-Uhlenbeck 
process
acts as a stochastic clock.


http://front.math.ucdavis.edu/math.PR/0503516

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3219. RECONSTRUCTING A TWO-COLOR SCENERY BY OBSERVING IT ALONG A SIMPLE 
RANDOM  WALK PATH

Heinrich Matzinger

Let {\xi (n)}_{n\in Z} be a two-color random scenery, that is, a random
coloring of Z in two colors, such that the \xi (i)'s are i.i.d. 
Bernoulli
variables with parameter \tfrac12. Let {S(n)}_{n\in N} be a symmetric 
random
walk starting at 0. Our main result shows that a.s., \xi \circ S (the
composition of \xi and S) determines \xi up to translation and 
reflection. In
other words, by observing the scenery \xi along the random walk path S, 
we can
a.s. reconstruct \xi up to translation and reflection. This result 
gives a
positive answer to the question of H. Kesten of whether one can a.s. 
detect a
single defect in almost every two-color random scenery by observing it 
only
along a random walk path.


http://front.math.ucdavis.edu/math.PR/0503517

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3220. A DIFFUSION MODEL OF SCHEDULING CONTROL IN QUEUEING SYSTEMS WITH 
MANY  SERVERS

Rami Atar

This paper studies a diffusion model that arises as the limit of a 
queueing
system scheduling problem in the asymptotic heavy traffic regime of 
Halfin and
Whitt. The queueing system consists of several customer classes and many
servers working in parallel, grouped in several stations. Servers in 
different
stations offer service to customers of each class at possibly different 
rates.
The control corresponds to selecting what customer class each server 
serves at
each time. The diffusion control problem does not seem to have explicit
solutions and therefore a characterization of optimal solutions via the
Hamilton-Jacobi-Bellman equation is addressed. Our main result is the 
existence
and uniqueness of solutions of the equation. Since the model is set on 
an
unbounded domain and the cost per unit time is unbounded, the analysis 
requires
estimates on the state process that are subexponential in the time 
variable. In
establishing these estimates, a key role is played by an integral 
formula that
relates queue length and idle time processes, which may be of 
independent
interest.


http://front.math.ucdavis.edu/math.PR/0503518

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3221. EXACT AND APPROXIMATE RESULTS FOR DEPOSITION AND ANNIHILATION 
PROCESSES  ON GRAPHS

Mathew D. Penrose and Aidan Sudbury

We consider random sequential adsorption processes where the initially 
empty
sites of a graph are irreversibly occupied, in random order, either by 
monomers
which block neighboring sites, or by dimers. We also consider a process 
where
initially occupied sites annihilate their neighbors at random times. We 
verify
that these processes are well defined on infinite graphs, and derive 
forward
equations governing joint vacancy/occupation probabilities. Using 
these, we
derive exact formulae for occupation probabilities and pair 
correlations in
Bethe lattices. For the blocking and annihilation processes we also 
prove
positive correlations between sites an even distance apart, and for 
blocking we
derive rigorous lower bounds for the site occupation probability in 
lattices,
including a lower bound of 1/3 for Z^2. We also give normal 
approximation
results for the number of occupied sites in a large finite graph.


http://front.math.ucdavis.edu/math.PR/0503519

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3222. NEAR-INTEGRATED GARCH SEQUENCES

Istvan Berkes and  Lajos Horvath and Piotr Kokoszka

Motivated by regularities observed in time series of returns on 
speculative
assets, we develop an asymptotic theory of GARCH(1,1) processes {y_k} 
defined
by the equations y_k=\sigma_k\epsilon_k, \sigma_k^2=\omega +\alpha
y_{k-1}^2+\beta \sigma_{k-1}^2 for which the sum \alpha +\beta 
approaches unity
as the number of available observations tends to infinity. We call such
sequences near-integrated. We show that the asymptotic behavior of
near-integrated GARCH(1,1) processes critically depends on the sign of 
\gamma
:=\alpha +\beta -1. We find assumptions under which the solutions 
exhibit
increasing oscillations and show that these oscillations grow 
approximately
like a power function if \gamma \leq 0 and exponentially if \gamma >0. 
We
establish an additive representation for the near-integrated GARCH(1,1)
processes which is more convenient to use than the traditional 
multiplicative
Volterra series expansion.


http://front.math.ucdavis.edu/math.PR/0503520

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3223. ASYMPTOTICS IN RANDOMIZED URN MODELS

Zhi-Dong Bai and Feifang Hu

This paper studies a very general urn model stimulated by designs in 
clinical
trials, where the number of balls of different types added to the urn 
at trial
n depends on a random outcome directed by the composition at trials
1,2,...,n-1. Patient treatments are allocated according to types of 
balls. We
establish the strong consistency and asymptotic normality for both the 
urn
composition and the patient allocation under general assumptions on 
random
generating matrices which determine how balls are added to the urn. 
Also we
obtain explicit forms of the asymptotic variance-covariance matrices of 
both
the urn composition and the patient allocation. The conditions on the
nonhomogeneity of generating matrices are mild and widely satisfied in
applications. Several applications are also discussed.


http://front.math.ucdavis.edu/math.PR/0503521

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3224. A BERRY-ESSEEN THEOREM FOR FEYNMAN-KAC AND INTERACTING PARTICLE 
MODELS

Pierre Del Moral and Samy Tindel

In this paper we investigate the speed of convergence of the 
fluctuations of
a general class of Feynman-Kac particle approximation models. We design 
an
original approach based on new Berry-Esseen type estimates for abstract
martingale sequences combined with original exponential concentration 
estimates
of interacting processes. These results extend the corresponding 
statements in
the classical theory and apply to a class of branching and genealogical
path-particle models arising in nonlinear filtering literature as well 
as in
statistical physics and biology.


http://front.math.ucdavis.edu/math.PR/0503522

---------------------------------------------------------------

3225. PERIODIC COPOLYMERS AT SELECTIVE INTERFACES: A LARGE DEVIATIONS 
APPROACH

Erwin Bolthausen and Giambattista Giacomin

We analyze a (1+1)-dimension directed random walk model of a polymer 
dipped
in a medium constituted by two immiscible solvents separated by a flat
interface. The polymer chain is heterogeneous in the sense that a single
monomer may energetically favor one or the other solvent. We focus on 
the case
in which the polymer types are periodically distributed along the chain 
or, in
other words, the polymer is constituted of identical stretches of fixed 
length.
The phenomenon that one wants to analyze is the localization at the 
interface:
energetically favored configurations place most of the monomers in the
preferred solvent and this can be done only if the polymer sticks close 
to the
interface. We investigate, by means of large deviations, the 
energy-entropy
competition that may lead, according to the value of the parameters (the
strength of the coupling between monomers and solvents and an asymmetry
parameter), to localization. We express the free energy of the system 
in terms
of a variational formula that we can solve. We then use the result to 
analyze
the phase diagram.


http://front.math.ucdavis.edu/math.PR/0503523

---------------------------------------------------------------

3226. HITTING DISTRIBUTIONS OF GEOMETRIC BROWNIAN MOTION

T. Byczkowski and M. Ryznar

Let $\tau$ be the first hitting time of the point 1 by the geometric 
Brownian
motion $X(t)= x \exp(B(t)-2\mu t)$ with drift $\mu \geq 0$ starting 
from $x>1$.
Here $B(t)$ is the Brownian motion starting from 0 with $E^0 B^2(t) = 
2t$. We
provide an integral formula for the density function of the stopped 
exponential
functional $A(\tau)=\int_0^\tau X^2(t) dt$ and determine its asymptotic
behaviour at infinity. Although we basically rely on methods developed 
in
\cite{BGS}, the present paper also covers the case of arbitrary drifts 
$\mu
\geq 0$ and provides a significant unification and extension of results 
of the
above-mentioned paper. As a corollary we provide an integral formula 
and give
asymptotic behaviour at infinity of the Poisson kernel for half-spaces 
for
Brownian motion with drift in real hyperbolic spaces of arbitrary 
dimension.


http://front.math.ucdavis.edu/math.PR/0503060

---------------------------------------------------------------

3227. MASS EXTINCTIONS: AN ALTERNATIVE TO THE ALLEE EFFECT

Rinaldo B. Schinazi

We introduce a spatial stochastic process on the lattice Z^d to model 
mass
extinctions. Each site of the lattice may host a flock of up to N 
individuals.
Each individual may give birth to a new individual at the same site at 
rate
\phi until the maximum of N individuals has been reached at the site. 
Once the
flock reaches N individuals, then, and only then, it starts giving 
birth on
each of the 2d neighboring sites at rate \lambda(N). Finally, disaster 
strikes
at rate 1, that is, the whole flock disappears. Our model shows that, 
at least
in theory, there is a critical maximum flock size above which a species 
is
certain to disappear and below which it may survive.


http://front.math.ucdavis.edu/math.PR/0503525

---------------------------------------------------------------

3228. TAIL OF A LINEAR DIFFUSION WITH MARKOV SWITCHING

Benoite de Saporta and Jian-Feng Yao

Let Y be an Ornstein-Uhlenbeck diffusion governed by a stationary and 
ergodic
Markov jump process X: dY_t=a(X_t)Y_t dt+\sigma(X_t) dW_t, Y_0=y_0. 
Ergodicity
conditions for Y have been obtained. Here we investigate the tail 
propriety of
the stationary distribution of this model. A characterization of either 
heavy
or light tail case is established. The method is based on a renewal 
theorem for
systems of equations with distributions on R.


http://front.math.ucdavis.edu/math.PR/0503527

---------------------------------------------------------------

3229. THE LONG-RUN BEHAVIOR OF THE STOCHASTIC REPLICATOR DYNAMICS

Lorens A. Imhof

Fudenberg and Harris' stochastic version of the classical replicator 
dynamics
is considered. The behavior of this diffusion process in the presence 
of an
evolutionarily stable strategy is investigated. Moreover, extinction of
dominated strategies and stochastic stability of strict Nash equilibria 
are
studied. The general results are illustrated in connection with a 
discrete war
of attrition. A persistence result for the maximum effort strategy is 
obtained
and an explicit expression for the evolutionarily stable strategy is 
derived.


http://front.math.ucdavis.edu/math.PR/0503529

---------------------------------------------------------------

3230. OPTIMAL POINTWISE APPROXIMATION OF SDES BASED ON BROWNIAN MOTION 
AT  DISCRETE POINTS

Thomas Muller-Gronbach

We study pathwise approximation of scalar stochastic differential 
equations
at a single point. We provide the exact rate of convergence of the 
minimal
errors that can be achieved by arbitrary numerical methods that are 
based (in a
measurable way) on a finite number of sequential observations of the 
driving
Brownian motion. The resulting lower error bounds hold in particular 
for all
methods that are implementable on a computer and use a random number 
generator
to simulate the driving Brownian motion at finitely many points. Our 
analysis
shows that approximation at a single point is strongly connected to an
integration problem for the driving Brownian motion with a random 
weight.
Exploiting general ideas from estimation of weighted integrals of 
stochastic
processes, we introduce an adaptive scheme, which is easy to implement 
and
performs asymptotically optimally.


http://front.math.ucdavis.edu/math.PR/0503531

---------------------------------------------------------------

3231. QUANTITATIVE BOUNDS ON CONVERGENCE OF TIME-INHOMOGENEOUS MARKOV 
CHAINS

R. Douc and  E. Moulines and Jeffrey S. Rosenthal

Convergence rates of Markov chains have been widely studied in recent 
years.
In particular, quantitative bounds on convergence rates have been 
studied in
various forms by Meyn and Tweedie [Ann. Appl. Probab. 4 (1994) 
981-1101],
Rosenthal [J. Amer. Statist. Assoc. 90 (1995) 558-566], Roberts and 
Tweedie
[Stochastic Process. Appl. 80 (1999) 211-229], Jones and Hobert 
[Statist. Sci.
16 (2001) 312-334] and Fort [Ph.D. thesis (2001) Univ. Paris VI]. In 
this
paper, we extend a result of Rosenthal [J. Amer. Statist. Assoc. 90 
(1995)
558-566] that concerns quantitative convergence rates for 
time-homogeneous
Markov chains. Our extension allows us to consider f-total variation 
distance
(instead of total variation) and time-inhomogeneous Markov chains. We 
apply our
results to simulated annealing.


http://front.math.ucdavis.edu/math.PR/0503532

---------------------------------------------------------------

3232. ON STATIONARITY OF LAGRANGIAN OBSERVATIONS OF PASSIVE TRACER 
VELOCITY IN  A COMPRESSIBLE ENVIRONMENT

Tomasz Komorowski and Grzegorz Krupa

We study the transport of a passive tracer particle in a steady strongly
mixing flow with a nonzero mean velocity. We show that there exists a
probability measure under which the particle Lagrangian velocity 
process is
stationary. This measure is absolutely continuous with respect to the
underlying probability measure for the Eulerian flow.


http://front.math.ucdavis.edu/math.PR/0503534

---------------------------------------------------------------

3233. EXTENDING CHACON-WALSH: MINIMALITY AND GENERALISED STARTING  
DISTRIBUTIONS

Alexander Cox

In this paper we consider the Skorokhod embedding problem for general
starting and target measures. In particular, we provide necessary and
sufficient conditions for a stopping time to be minimal in the sense of
Monroe(1972). The resulting conditions have a nice interpretation in the
graphical picture of Chacon and Walsh. Further, we demonstrate how the
construction of Chacon and Walsh can be extended to any (integrable) 
starting
and target distributions, allowing the constructions of Azema-Yor, 
Vallois and
Jacka to be viewed in this context, and thus extended easily to general
starting and target distributions. In particular, we describe in detail 
the
extension of the Azema-Yor embedding in this context, and show that it 
retains
its optimality property.


http://front.math.ucdavis.edu/math.PR/0503535

---------------------------------------------------------------

3234. EXPONENTIAL PENALTY FUNCTION CONTROL OF LOSS NETWORKS

Garud Iyengar and Karl Sigman

We introduce penalty-function-based admission control policies to
approximately maximize the expected reward rate in a loss network. These
control policies are easy to implement and perform well both in the 
transient
period as well as in steady state. A major advantage of the penalty 
approach is
that it avoids solving the associated dynamic program. However, a 
disadvantage
of this approach is that it requires the capacity requested by 
individual
requests to be sufficiently small compared to total available capacity. 
We
first solve a related deterministic linear program (LP) and then 
translate an
optimal solution of the LP into an admission control policy for the loss
network via an exponential penalty function. We show that the penalty 
policy is
a target-tracking policy--it performs well because the optimal solution 
of the
LP is a good target. We demonstrate that the penalty approach can be 
extended
to track arbitrarily defined target sets. Results from preliminary 
simulation
studies are included.


http://front.math.ucdavis.edu/math.PR/0503536

---------------------------------------------------------------

3235. ELEMENTARY BOUNDS ON POINCARE AND LOG-SOBOLEV CONSTANTS FOR 
DECOMPOSABLE  MARKOV CHAINS

Mark Jerrum and  Jung-Bae Son and  Prasad Tetali and Eric Vigoda

We consider finite-state Markov chains that can be naturally decomposed 
into
smaller ``projection'' and ``restriction'' chains. Possibly this 
decomposition
will be inductive, in that the restriction chains will be smaller 
copies of the
initial chain. We provide expressions for Poincare (resp. log-Sobolev)
constants of the initial Markov chain in terms of Poincare (resp. 
log-Sobolev)
constants of the projection and restriction chains, together with 
further a
parameter. In the case of the Poincare constant, our bound is always at 
least
as good as existing ones and, depending on the value of the extra 
parameter,
may be much better. There appears to be no previously published 
decomposition
result for the log-Sobolev constant. Our proofs are elementary and
self-contained.


http://front.math.ucdavis.edu/math.PR/0503537

---------------------------------------------------------------

3236. RUIN PROBABILITIES AND OVERSHOOTS FOR GENERAL LEVY INSURANCE RISK 
  PROCESSES

Claudia Kluppelberg and  Andreas E. Kyprianou and Ross A. Maller

We formulate the insurance risk process in a general Levy process 
setting,
and give general theorems for the ruin probability and the asymptotic
distribution of the overshoot of the process above a high level, when 
the
process drifts to -\infty a.s. and the positive tail of the Levy 
measure, or of
the ladder height measure, is subexponential or, more generally, 
convolution
equivalent. Results of Asmussen and Kluppelberg [Stochastic Process. 
Appl. 64
(1996) 103-125] and Bertoin and Doney [Adv. in Appl. Probab. 28 (1996) 
207-226]
for ruin probabilities and the overshoot in random walk and compound 
Poisson
models are shown to have analogues in the general setup. The identities 
we
derive open the way to further investigation of general renewal-type 
properties
of Levy processes.


http://front.math.ucdavis.edu/math.PR/0503539

---------------------------------------------------------------

3237. COMBINATORIAL ASPECTS OF MATRIX MODELS

Alice Guionnet and \'Edouard Maurel-Segala

We show that under reasonably general assumptions, the first order
asymptotics of the free energy of matrix models are generating 
functions for
colored planar maps. This is based on the fact that solutions of the
differential Schwinger-Dyson equations are, by nature, generating 
functions for
enumerating planar maps, a remark which bypasses the use of Gaussian 
calculus.


http://front.math.ucdavis.edu/math.PR/0503064

---------------------------------------------------------------

3238. STABILITY IN DISTRIBUTION OF RANDOMLY PERTURBED QUADRATIC MAPS AS 
MARKOV  PROCESSES

Rabi Bhattacharya and Mukul Majumdar

Iteration of randomly chosen quadratic maps defines a Markov process:
X_{n+1}=\epsilon_{n+1}X_n(1-X_n), where \epsilon_n are i.i.d. with 
values in
the parameter space [0,4] of quadratic maps F_{\theta}(x)=\theta 
x(1-x). Its
study is of significance as an important Markov model, with 
applications to
problems of optimization under uncertainty arising in economics. In this
article a broad criterion is established for positive Harris recurrence 
of X_n.


http://front.math.ucdavis.edu/math.PR/0503540

---------------------------------------------------------------

3239. INTERPLAY BETWEEN DIVIDEND RATE AND BUSINESS CONSTRAINTS FOR A 
FINANCIAL  CORPORATION

Tahir Choulli and  Michael Taksar and Xun Yu Zhou

We study a model of a corporation which has the possibility to choose 
various
production/business policies with different expected profits and risks. 
In the
model there are restrictions on the dividend distribution rates as well 
as
restrictions on the risk the company can undertake. The objective is to
maximize the expected present value of the total dividend 
distributions. We
outline the corresponding Hamilton-Jacobi-Bellman equation, compute 
explicitly
the optimal return function and determine the optimal policy. As a 
consequence
of these results, the way the dividend rate and business constraints 
affect the
optimal policy is revealed. In particular, we show that under certain
relationships between the constraints and the exogenous parameters of 
the
random processes that govern the returns, some business activities 
might be
redundant, that is, under the optimal policy they will never be used in 
any
scenario.


http://front.math.ucdavis.edu/math.PR/0503541

---------------------------------------------------------------

3240. LIMIT THEOREMS FOR MIXED MAX-SUM PROCESSES WITH RENEWAL STOPPING

Dmitrii S. Silvestrov and Jozef L. Teugels

This article is devoted to the investigation of limit theorems for mixed
max-sum processes with renewal type stopping indexes. Limit theorems of 
weak
convergence type are obtained as well as functional limit theorems.


http://front.math.ucdavis.edu/math.PR/0503543

---------------------------------------------------------------

3241. CONTINUUM PERCOLATION WITH STEPS IN AN ANNULUS

Paul Balister and  Bela Bollobas and Mark Walters

Let A be the annulus in R^2 centered at the origin with inner and outer 
radii
r(1-\epsilon) and r, respectively. Place points {x_i} in R^2 according 
to a
Poisson process with intensity 1 and let G_A be the random graph with 
vertex
set {x_i} and edges x_ix_j whenever x_i-x_j\in A. We show that if the 
area of A
is large, then G_A almost surely has an infinite component. Moreover, 
if we fix
\epsilon, increase r and let n_c=n_c(\epsilon) be the area of A when 
this
infinite component appears, then n_c\to1 as \epsilon \to 0. This is in 
contrast
to the case of a ``square'' annulus where we show that n_c is bounded 
away from
1.


http://front.math.ucdavis.edu/math.PR/0503544

---------------------------------------------------------------

3242. A MICROSCOPIC PROBABILISTIC DESCRIPTION OF A LOCALLY REGULATED  
POPULATION AND MACROSCOPIC APPROXIMATIONS

Nicolas Fournier and Sylvie Meleard

We consider a discrete model that describes a locally regulated spatial
population with mortality selection. This model was studied in parallel 
by
Bolker and Pacala and Dieckmann, Law and Murrell. We first generalize 
this
model by adding spatial dependence. Then we give a pathwise description 
in
terms of Poisson point measures. We show that different normalizations 
may lead
to different macroscopic approximations of this model. The first 
approximation
is deterministic and gives a rigorous sense to the number density. The 
second
approximation is a superprocess previously studied by Etheridge. 
Finally, we
study in specific cases the long time behavior of the system and of its
deterministic approximation.


http://front.math.ucdavis.edu/math.PR/0503546

---------------------------------------------------------------

3243. STABILITY AND THE LYAPOUNOV EXPONENT OF THRESHOLD AR-ARCH MODELS

Daren B. H. Cline and Huay-min H. Pu

The Lyapounov exponent and sharp conditions for geometric ergodicity are
determined of a time series model with both a threshold autoregression 
term and
threshold autoregressive conditional heteroscedastic (ARCH) errors.
  The conditions require studying or simulating the behavior of a 
bounded,
ergodic Markov chain. The method of proof is based on a new approach, 
called
the piggyback method, that exploits the relationship between the time 
series
and the bounded chain. The piggyback method also provides a means for
evaluating the Lyapounov exponent by simulation and provides a new 
perspective
on moments, illuminating recent results for the distribution tails of 
GARCH
models.


http://front.math.ucdavis.edu/math.PR/0503547

---------------------------------------------------------------

3244. NORMAL APPROXIMATION FOR HIERARCHICAL STRUCTURES

Larry Goldstein

Given F:[a,b]^k\to [a,b] and a nonconstant X_0 with P(X_0\in [a,b])=1, 
define
the hierarchical sequence of random variables {X_n}_{n\ge 0} by
X_{n+1}=F(X_{n,1},...,X_{n,k}), where X_{n,i} are i.i.d. as X_n. Such 
sequences
arise from hierarchical structures which have been extensively studied 
in the
physics literature to model, for example, the conductivity of a random 
medium.
Under an averaging and smoothness condition on nontrivial F, an upper 
bound of
the form C\gamma^n for 0<\gamma<1 is obtained on the Wasserstein 
distance
between the standardized distribution of X_n and the normal. The 
results apply,
for instance, to random resistor networks and, introducing the notion 
of strict
averaging, to hierarchical sequences generated by certain compositions. 
As an
illustration, upper bounds on the rate of convergence to the normal are 
derived
for the hierarchical sequence generated by the weighted diamond lattice 
which
is shown to exhibit a full range of convergence rate behavior.


http://front.math.ucdavis.edu/math.PR/0503549

---------------------------------------------------------------

3245. ON THE SUPER REPLICATION PRICE OF UNBOUNDED CLAIMS

Sara Biagini and Marco Frittelli

In an incomplete market the price of a claim f in general cannot be 
uniquely
identified by no arbitrage arguments. However, the ``classical'' super
replication price is a sensible indicator of the (maximum selling) 
value of the
claim. When f satisfies certain pointwise conditions (e.g., f is 
bounded from
below), the super replication price is equal to sup_QE_Q[f], where Q 
varies on
the whole set of pricing measures. Unfortunately, this price is often 
too high:
a typical situation is here discussed in the examples. We thus define 
the less
expensive weak super replication price and we relax the requirements on 
f by
asking just for ``enough'' integrability conditions. By building up a 
proper
duality theory, we show its economic meaning and its relation with the
investor's preferences. Indeed, it turns out that the weak super 
replication
price of f coincides with sup_{Q\in M_{\Phi}}E_Q[f], where M_{\Phi} is 
the
class of pricing measures with finite generalized entropy (i.e., E[\Phi
(\frac{dQ}{dP})]<\infty) and where \Phi is the convex conjugate of the 
utility
function of the investor.


http://front.math.ucdavis.edu/math.PR/0503550

---------------------------------------------------------------

3246. LIMIT LAWS OF ESTIMATORS FOR CRITICAL MULTI-TYPE GALTON-WATSON 
PROCESSES

Zhiyi Chi

We consider the asymptotics of various estimators based on a large 
sample of
branching trees from a critical multi-type Galton-Watson process, as 
the sample
size increases to infinity. The asymptotics of additive functions of 
trees,
such as sizes of trees and frequencies of types within trees, a 
higher-order
asymptotic of the ``relative frequency'' estimator of the left 
eigenvector of
the mean matrix, a higher-order joint asymptotic of the maximum 
likelihood
estimators of the offspring probabilities and the consistency of an 
estimator
of the right eigenvector of the mean matrix, are established.


http://front.math.ucdavis.edu/math.PR/0503552

---------------------------------------------------------------

3247. ON SAMPLING OF STATIONARY INCREMENT PROCESSES

J. M. P. Albin

Under a complex technical condition, similar to such used in extreme 
value
theory, we find the rate q(\epsilon)^{-1} at which a stochastic process 
with
stationary increments \xi should be sampled, for the sampled process
\xi(\lfloor\cdot /q(\epsilon)\rfloor q(\epsilon)) to deviate from \xi 
by at
most \epsilon, with a given probability, asymptotically as \epsilon
\downarrow0. The canonical application is to discretization errors in 
computer
simulation of stochastic processes.


http://front.math.ucdavis.edu/math.PR/0503554

---------------------------------------------------------------

3248. RECURRENCE OF SIMPLE RANDOM WALK ON $Z^2$ IS DYNAMICALLY SENSITIVE

Christopher Hoffman

Benjamini, Haggstrom, Peres and Steif introduced the concept of a 
dynamical
random walk. This is a continuous family of random walks, {S_n(t)}. 
Benjamini
et. al. proved that if d=3 or d=4 then there is an exceptional set of t 
such
that {S_n(t)} returns to the origin infinitely often. In this paper we 
consider
a dynamical random walk on Z^2. We show that with probability one there 
exists
t such that {S_n(t)} never returns to the origin. This exceptional set 
of times
has dimension one. This proves a conjecture of Benjamini et. al.


http://front.math.ucdavis.edu/math.PR/0503065

---------------------------------------------------------------

3249. SPECTRAL PROPERTIES OF THE TANDEM JACKSON NETWORK, SEEN AS A  
QUASI-BIRTH-AND-DEATH PROCESS

D. P. Kroese and  W. R. W. Scheinhardt and P. G. Taylor

Quasi-birth-and-death (QBD) processes with infinite ``phase spaces'' can
exhibit unusual and interesting behavior. One of the simplest examples 
of such
a process is the two-node tandem Jackson network, with the ``phase'' 
giving the
state of the first queue and the ``level'' giving the state of the 
second
queue. In this paper, we undertake an extensive analysis of the 
properties of
this QBD. In particular, we investigate the spectral properties of 
Neuts's
R-matrix and show that the decay rate of the stationary distribution of 
the
``level'' process is not always equal to the convergence norm of R. In 
fact, we
show that we can obtain any decay rate from a certain range by 
controlling only
the transition structure at level zero, which is independent of R. We 
also
consider the sequence of tandem queues that is constructed by 
restricting the
waiting room of the first queue to some finite capacity, and then 
allowing this
capacity to increase to infinity. We show that the decay rates for the 
finite
truncations converge to a value, which is not necessarily the decay 
rate in the
infinite waiting room case. Finally, we show that the probability that 
the
process hits level n before level 0 given that it starts in level 1 
decays at a
rate which is not necessarily the same as the decay rate for the 
stationary
distribution.


http://front.math.ucdavis.edu/math.PR/0503555

---------------------------------------------------------------

3250. NUMBER OF PATHS VERSUS NUMBER OF BASIS FUNCTIONS IN AMERICAN 
OPTION  PRICING

Paul Glasserman and Bin Yu

An American option grants the holder the right to select the time at 
which to
exercise the option, so pricing an American option entails solving an 
optimal
stopping problem. Difficulties in applying standard numerical methods to
complex pricing problems have motivated the development of techniques 
that
combine Monte Carlo simulation with dynamic programming. One class of 
methods
approximates the option value at each time using a linear combination 
of basis
functions, and combines Monte Carlo with backward induction to estimate 
optimal
coefficients in each approximation. We analyze the convergence of such 
a method
as both the number of basis functions and the number of simulated paths
increase. We get explicit results when the basis functions are 
polynomials and
the underlying process is either Brownian motion or geometric Brownian 
motion.
We show that the number of paths required for worst-case convergence 
grows
exponentially in the degree of the approximating polynomials in the 
case of
Brownian motion and faster in the case of geometric Brownian motion.


http://front.math.ucdavis.edu/math.PR/0503556

---------------------------------------------------------------

3251. STOCHASTIC CHARACTERIZATION OF HARMONIC MAPS ON RIEMANNIAN 
POLYHEDRA

M. A. Aprodu and  T. Bouziane

The aim of this paper is to relate the theory of Harmonicity in sense
Korevaar-Schoen and Eells-Fuglede to the notion of a Brownian motion in
riemannian polyhedra achieved by the second author. Firstly, we prove 
that
Brownian motions is stochastically continuous Markov processes and 
consequently
it has a unique infinitesimal generator on some Banach space. Secondly, 
we show
that in some sense, the Brownian motion in Riemannian polyhedra has as 
an
infinitesimal generator the "Laplacian". Finally, we show that harmonic 
maps,
with target smooth Riemannian manifolds, in the sense of Eells-Fuglede, 
are
exactly those which maps Brownian motion in Riemannian polyhedron into a
martingale, while harmonic morphisms are exactly the maps which are 
Brownian
preserving paths


http://front.math.ucdavis.edu/math.PR/0503557

---------------------------------------------------------------

3252. CENTRAL LIMIT THEOREMS FOR RANDOM POLYTOPES IN A SMOOTH CONVEX SET

Van Vu

Let $K$ be a smooth convex set with volume one in $\BBR^d$. Choose $n$ 
random
points in $K$ independently according to the uniform distribution. The 
convex
hull of these points, denoted by $K_n$, is called a {\it random 
polytope}. We
prove that several key functionals of $K_n$ satisfy the central limit 
theorem
as $n$ tends to infinity.


http://front.math.ucdavis.edu/math.PR/0503559

---------------------------------------------------------------

3253. QUENCHED INVARIANCE PRINCIPLE FOR SIMPLE RANDOM WALK ON 
TWO-DIMENSIONAL  PERCOLATION CLUSTERS

Noam Berger and Marek Biskup

We consider the simple random walk on a two-dimensional super-critical
infinite percolation cluster and prove that for almost every 
configuration it
scales to Brownian motion.


http://front.math.ucdavis.edu/math.PR/0503576

---------------------------------------------------------------

3254. ASYMPTOTIC GENEALOGY OF A CRITICAL BRANCHING PROCESS

Lea Popovic

Consider a continuous-time binary branching process conditioned to have
population size n at some time t, and with a chance p for recording each
extinct individual in the process. Within the family tree of this 
process, we
consider the smallest subtree containing the genealogy of the extant
individuals together with the genealogy of the recorded extinct 
individuals. We
introduce a novel representation of such subtrees in terms of a 
point-process,
and provide asymptotic results on the distribution of this 
point-process as the
number of extant individuals increases. We motivate the study within 
the scope
of a coherent analysis for an a priori model for macroevolution.


http://front.math.ucdavis.edu/math.PR/0503577

---------------------------------------------------------------

3255. GENERALIZED STOCHASTIC DIFFERENTIAL UTILITY AND PREFERENCE FOR  
INFORMATION

Ali Lazrak

This paper develops, in a Brownian information setting, an approach for
analyzing the preference for information, a question that motivates the
stochastic differential utility (SDU) due to Duffie and Epstein 
[Econometrica
60 (1992) 353-394]. For a class of backward stochastic differential 
equations
(BSDEs) including the generalized SDU [Lazrak and Quenez Math. Oper. 
Res. 28
(2003) 154-180], we formulate the information neutrality property as an
invariance principle when the filtration is coarser (or finer) and 
characterize
it. We also provide concrete examples of heterogeneity in information 
that
illustrate explicitly the nonneutrality property for some GSDUs. Our 
results
suggest that, within the GSDUs class of intertemporal utilities, risk 
aversion
or ambiguity aversion are inflexibly linked to the preference for 
information.


http://front.math.ucdavis.edu/math.PR/0503579

---------------------------------------------------------------

3256. THE RIGHT TIME TO SELL A STOCK WHOSE PRICE IS DRIVEN BY MARKOVIAN 
NOISE

Robert C. Dalang and M.-O. Hongler

We consider the problem of finding the optimal time to sell a stock, 
subject
to a fixed sales cost and an exponential discounting rate \rho. We 
assume that
the price of the stock fluctuates according to the equation dY_t=Y_t(\mu
dt+\sigma\xi(t) dt), where (\xi(t)) is an alternating Markov renewal 
process
with values in {\pm1}, with an exponential renewal time. We determine 
the
critical value of \rho under which the value function is finite. We 
examine the
validity of the ``principle of smooth fit'' and use this to give a 
complete and
essentially explicit solution to the problem, which exhibits a 
surprisingly
rich structure. The corresponding result when the stock price evolves 
according
to the Black and Scholes model is obtained as a limit case.


http://front.math.ucdavis.edu/math.PR/0503580

---------------------------------------------------------------

3257. CONCENTRATION OF NORMALIZED SUMS AND A CENTRAL LIMIT THEOREM FOR  
NONCORRELATED RANDOM VARIABLES

Sergey G. Bobkov

For noncorrelated random variables, we study a concentration property 
of the
family of distributions of normalized sums formed by sequences of times 
of a
given large length.


http://front.math.ucdavis.edu/math.PR/0503583

---------------------------------------------------------------

3258. ANALYSIS OF A CLASS OF LIKELIHOOD BASED CONTINUOUS TIME 
STOCHASTIC  VOLATILITY MODELS INCLUDING ORNSTEIN-UHLENBECK MODELS IN 
FINANCIAL ECONOMICS

Lancelot F. James

In a series of recent papers Barndorff-Nielsen and Shephard introduce an
attractive class of continuous time stochastic volatility models for 
financial
assets where the volatility processes are functions of positive
Ornstein-Uhlenbeck(OU) processes. This models are known to be 
substantially
more flexible than Gaussian based models. One current problem of this 
approach
is the unavailability of a tractable exact analysis of likelihood based
stochastic volatility models for the returns of log prices of stocks.
   With this point in mind, the likelihood models of Barndorff-Nielsen 
and
Shephard are viewed as members of a much larger class of models. That is
likelihoods based on n conditionally independent Normal random 
variables whose
mean and variance are representable as linear functionals of a common
unobserved Poisson random measure. The analysis of these models is 
facilitated
by applying the methods in James (2005, 2002), in particular an Esscher 
type
transform of Poisson random measures; in conjunction with a special 
case of the
Weber-Sonine formula. It is shown that the marginal likelihood may be 
expressed
in terms of a multidimensional Fourier-cosine transform. This yields 
tractable
forms of the likelihood and also allows a full Bayesian posterior 
analysis of
the integrated volatility process. A general formula for the posterior 
density
of the log price given the observed data is derived, which could 
potentially
have applications to option pricing. We also identify tractable 
subclasses,
where inference can be based on a finite number of independent random
variables. It is shown that inference does not necessarily require 
simulation
of random measures. Rather, classical numerical integration can be used 
in the
most general cases.


http://front.math.ucdavis.edu/math.ST/0503055

---------------------------------------------------------------

3259. MODIFIED LOGARITHMIC SOBOLEV INEQUALITIES IN NULL CURVATURE

Ivan Gentil and  Arnaud Guillin and Laurent Miclo

We present a logarithmic Sobolev inequality adapted to a log-concave 
measure.
Assume that $\Phi$ is a symmetric convex function on $\dR$ satisfying
$(1+\e)\Phi(x)\leq {x}\Phi'(x)\leq(2-\e)\Phi(x)$ for $x\geq0$ large 
enough and
with $\e\in]0,1/2]$. We prove that the probability measure on $\dR$
$\mu_\Phi(dx)=e^{-\Phi(x)}/Z_\Phi dx$ satisfies a modified and adapted
logarithmic Sobolev inequality : there exist three constant $A,B,D>0$ 
such that
for all smooth $f>0$, \begin{equation*}
   \ent{\mu_\Phi}{f^2}\leq A\int 
H_{\Phi}\PAR{{\frac{f'}{f}}}f^2d\mu_\Phi,
\text{with} H_{\Phi}(x)= {\begin{array}{rl} \Phi^*\PAR{Bx} &\text{if
}\ABS{x}\geq D, x^2 &\text{if}\ABS{x}\leq D. \end{array} . 
\end{equation*}


http://front.math.ucdavis.edu/math.PR/0503585

---------------------------------------------------------------

3260. LENSES IN SKEW BROWNIAN FLOW

Krzysztof Burdzy and Haya Kaspi

We consider a stochastic flow in which individual particles follow skew
Brownian motions, with each one of these processes driven by the same 
Brownian
motion. One does not have uniqueness for the solutions of the 
corresponding
stochastic differential equation simultaneously for all real initial
conditions. Due to this lack of the simultaneous strong uniqueness for 
the
whole system of stochastic differential equations, the flow contains 
lenses,
that is, pairs of skew Brownian motions which start at the same point,
bifurcate, and then coalesce in a finite time. The paper contains 
qualitative
and quantitative (distributional) results on the geometry of the flow 
and
lenses.


http://front.math.ucdavis.edu/math.PR/0503586

---------------------------------------------------------------

3261. WEAK POINCARE INEQUALITIES ON DOMAINS DEFINED BY BROWNIAN ROUGH 
PATHS

Shigeki Aida

We prove weak Poincare inequalities on domains which are inverse images 
of
open sets in Wiener spaces under continuous functions of Brownian rough 
paths.
The result is applicable to Dirichlet forms on loop groups and 
connected open
subsets of path spaces over compact Riemannian manifolds.


http://front.math.ucdavis.edu/math.PR/0503587

---------------------------------------------------------------

3262. TIME CHANGES OF SYMMETRIC DIFFUSIONS AND FELLER MEASURES

Masatoshi Fukushima and  Ping He and Jiangang Ying

We extend the classical Douglas integral, which expresses the Dirichlet
integral of a harmonic function on the unit disk in terms of its value 
on
boundary, to the case of conservative symmetric diffusion in terms of 
Feller
measure, by using the approach of time change of Markov processes.


http://front.math.ucdavis.edu/math.PR/0503588

---------------------------------------------------------------

3263. DIFFERENCE PROPHET INEQUALITIES FOR [0,1]-VALUED I.I.D. RANDOM 
VARIABLES  WITH COST FOR OBSERVATIONS

Holger Kosters

Let X_1,X_2,... be a sequence of [0,1]-valued i.i.d. random variables, 
let
c\geq 0 be a sampling cost for each observation and let Y_i=X_i-ic, 
i=1,2,....
For n=1,2,..., let M(Y_1,...,Y_n)=E(max_{1\leq i\leq n}Y_i) and
V(Y_1,...,Y_n)=sup_{\tau \in C^n}E(Y_{\tau}), where C^n denotes the set 
of all
stopping rules for Y_1,...,Y_n. Sharp upper bounds for the difference
M(Y_1,...,Y_n)-V(Y_1,...,Y_n) are given under various restrictions on c 
and n.


http://front.math.ucdavis.edu/math.PR/0503589

---------------------------------------------------------------

3264. UNIQUENESS FOR DIFFUSIONS DEGENERATING AT THE BOUNDARY OF A 
SMOOTH  BOUNDED SET

Dante DeBlassie

For continuous \gamma, g:[0,1]\to(0,\infty), consider the degenerate
stochastic differential equation dX_t=[1-|X_t|^2]^{1/2}\gamma(|X_t|)
dB_t-g(|X_t|)X_t dt in the closed unit ball of R^n. We introduce a new 
idea to
show pathwise uniqueness holds when \gamma and g are Lipschitz and
\frac{g(1)}{\gamma^2(1)}>\sqrt2-1. When specialized to a case studied 
by Swart
[Stochastic Process. Appl. 98 (2002) 131-149] with \gamma=\sqrt2 and 
g\equiv c,
this gives an improvement of his result. Our method applies to more 
general
contexts as well. Let D be a bounded open set with C^3 boundary and 
suppose
h:\barD\to R Lipschitz on \barD, as well as C^2 on a neighborhood of 
\partial D
with Lipschitz second partials there. Also assume h>0 on D, h=0 on 
\partial D
and |\nabla h|>0 on \partial D. An example of such a function is
h(x)=d(x,\partial D). We give conditions which ensure pathwise 
uniqueness holds
for dX_t=h(X_t)^{1/2}\sigma(X_t) dB_t+b(X_t) dt in \barD.


http://front.math.ucdavis.edu/math.PR/0503590

---------------------------------------------------------------

3265. MODERATE DEVIATIONS FOR DIFFUSIONS WITH BROWNIAN POTENTIALS

Yueyun Hu and Zhan Shi

We present precise moderate deviation probabilities, in both quenched 
and
annealed settings, for a recurrent diffusion process with a Brownian 
potential.
Our method relies on fine tools in stochastic calculus, including 
Kotani's
lemma and Lamperti's representation for exponential functionals. In 
particular,
our result for quenched moderate deviations is in agreement with a 
recent
theorem of Comets and Popov [Probab. Theory Related Fields 126 (2003) 
571-609]
who studied the corresponding problem for Sinai's random walk in random
environment.


http://front.math.ucdavis.edu/math.PR/0503591

---------------------------------------------------------------

3266. SELF-INTERSECTION LOCAL TIME: CRITICAL EXPONENT, LARGE 
DEVIATIONS, AND  LAWS OF THE ITERATED LOGARITHM

Richard F. Bass and Xia Chen

If \beta_t is renormalized self-intersection local time for planar 
Brownian
motion, we characterize when Ee^{\gamma\beta_1} is finite or infinite 
in terms
of the best constant of a Gagliardo-Nirenberg inequality. We prove large
deviation estimates for \beta_1 and -\beta_1. We establish lim sup and 
lim inf
laws of the iterated logarithm for \beta_t as t\to\infty.


http://front.math.ucdavis.edu/math.PR/0503592

---------------------------------------------------------------

3267. EXPONENTIAL ASYMPTOTICS AND LAW OF THE ITERATED LOGARITHM FOR  
INTERSECTION LOCAL TIMES OF RANDOM WALKS

Xia Chen

Let \alpha ([0,1]^p) denote the intersection local time of p independent
d-dimensional Brownian motions running up to the time 1. Under the 
conditions
p(d-2)<d and d\ge 2, we prove lim_{t\to\infty}t^{-1}\log
P\bigl{\alpha([0,1]^p)\ge t^{(d(p-1))/2}\bigr}=-\gamma_{\alpha}(d,p) 
with the
right-hand side being identified in terms of the the best constant of 
the
Gagliardo-Nirenberg inequality. Within the scale of moderate 
deviations, we
also establish the precise tail asymptotics for the intersection local 
time
I_n=#{(k_1,...,k_p)\in [1,n]^p;S_1(k_1)=... =S_p(k_p)} run by the 
independent,
symmetric, Z^d-valued random walks S_1(n),...,S_p(n). Our results apply 
to the
law of the iterated logarithm. Our approach is based on Feynman-Kac 
type large
deviation, time exponentiation, moment computation and some 
technologies along
the lines of probability in Banach space. As an interesting coproduct, 
we
obtain the inequality \bigl(EI_{n_1+... +n_a}^m\bigr)^{1/p}\le 
\sum_{k_1+...
+k_a=m\limits_{k_1,...,k_a\ge 0}}\frac{m!}{k_1!...
k_a!}\bigl(EI_{n_1}^{k_1}\bigr)^{1/p}... 
\bigl(EI_{n_a}^{k_a}\bigr)^{1/p} in
the case of random walks.


http://front.math.ucdavis.edu/math.PR/0503593

---------------------------------------------------------------

3268. REGULARITY OF SOLUTIONS TO STOCHASTIC VOLTERRA EQUATIONS WITH 
INFINITE  DELAY

Anna Karczewska and  Carlos Lizama

The paper gives necessary and sufficient conditions providing 
regularity of
solutions to stochastic Volterra equations with infinite delay on a
$d$-dimensional torus. The harmonic analysis techniques and stochastic
integration in function spaces are used.


http://front.math.ucdavis.edu/math.PR/0503595

---------------------------------------------------------------

3269. A CLASS OF GENERALIZED HYPERBOLIC CONTINUOUS TIME INTEGRATED 
STOCHASTIC  VOLATILITY LIKELIHOOD MODELS

Lancelot F. James and John W. Lau

This paper discusses and analyzes a class of likelihood models which are
based on two distributional innovations in financial models for stock 
returns.
That is, the notion that the marginal distribution of aggregate returns 
of
log-stock prices are well approximated by generalized hyperbolic 
distributions,
and that volatility clustering can be handled by specifying the 
integrated
volatility as a random process such as that proposed in a recent series 
of
papers by Barndorff-Nielsen and Shephard (BNS). The BNS models produce
likelihoods for aggregate returns which can be viewed as a subclass of 
latent
regression models where one has n conditionally independent Normal 
random
variables whose mean and variance are representable as linear 
functionals of a
common unobserved Poisson random measure. James (2005b) recently 
obtains an
exact analysis for such models yielding expressions of the likelihood 
in terms
of quite tractable Fourier-Cosine integrals. Here, our idea is to 
analyze a
class of likelihoods, which can be used for similar purposes, but where 
the
latent regression models are based on n conditionally independent 
models with
distributions belonging to a subclass of the generalized hyperbolic
distributions and whose corresponding parameters are representable as 
linear
functionals of a common unobserved Poisson random measure. Our models 
are
perhaps most closely related to the Normal inverse 
Gaussian/GARCH/A-PARCH
models of Brandorff-Nielsen (1997) and Jensen and Lunde (2001), where 
in our
case the GARCH component is replaced by quantities such as INT-OU 
processes. It
is seen that, importantly, such likelihood models exhibit quite 
different
features structurally. One nice feature of the model is that it allows 
for more
flexibility in terms of modelling of external regression parameters.


http://front.math.ucdavis.edu/math.ST/0503056

---------------------------------------------------------------

3270. A LOCAL LIMIT THEOREM FOR DIRECTED POLYMERS IN RANDOM MEDIA: THE  
CONTINUOUS AND THE DISCRETE CASE

Vincent Vargas (PMA)

In this article, we consider two models of directed polymers in random
environment: a discrete model and a continuous model. We consider these 
models
in dimension greater or equal to 3 and we suppose that the normalized 
partition
function is bounded in L^2. Under these assumptions, Sinai proved a 
local limit
theorem for the discrete model, using a perturbation expansion. In this
article, we give a new method for proving Sinai's local limit theorem. 
This new
method can be transposed to the continuous setting in which we prove a 
similar
local limit theorem.


http://front.math.ucdavis.edu/math.PR/0503596

---------------------------------------------------------------

3271. GLOBAL L_2-SOLUTIONS OF STOCHASTIC NAVIER-STOKES EQUATIONS

R. Mikulevicius and B. L. Rozovskii

This paper concerns the Cauchy problem in R^d for the stochastic
Navier-Stokes equation \partial_tu=\Delta u-(u,\nabla)u-\nabla p+f(u)+
[(\sigma,\nabla)u-\nabla \tilde p+g(u)]\circ \dot W, u(0)=u_0,\qquad 
divu=0,
driven by white noise \dot W. Under minimal assumptions on regularity 
of the
coefficients and random forces, the existence of a global weak 
(martingale)
solution of the stochastic Navier-Stokes equation is proved. In the
two-dimensional case, the existence and pathwise uniqueness of a global 
strong
solution is shown. A Wiener chaos-based criterion for the existence and
uniqueness of a strong global solution of the Navier-Stokes equations is
established.


http://front.math.ucdavis.edu/math.PR/0503597

---------------------------------------------------------------

3272. CENTRAL LIMIT THEOREMS FOR SEQUENCES OF MULTIPLE STOCHASTIC 
INTEGRALS

David Nualart and Giovanni Peccati

We characterize the convergence in distribution to a standard normal 
law for
a sequence of multiple stochastic integrals of a fixed order with 
variance
converging to 1. Some applications are given, in particular to study the
limiting behavior of quadratic functionals of Gaussian processes.


http://front.math.ucdavis.edu/math.PR/0503598

---------------------------------------------------------------

3273. STOCHASTIC INTEGRAL REPRESENTATION AND REGULARITY OF THE DENSITY 
FOR THE  EXIT MEASURE OF SUPER-BROWNIAN MOTION

Jean-Francois Le Gall and Leonid Mytnik

This paper studies the regularity properties of the density of the exit
measure for super-Brownian motion with (1+\beta)-stable branching 
mechanism. It
establishes the continuity of the density in dimension d=2 and the
unboundedness of the density in all other dimensions where the density 
exists.
An alternative description of the exit measure and its density is also 
given
via a stochastic integral representation. Results are applied to the
probabilistic representation of nonnegative solutions of the partial
differential equation \Delta u=u^{1+\beta}.


http://front.math.ucdavis.edu/math.PR/0503599

---------------------------------------------------------------

3274. PRECISE ASYMPTOTICS OF SMALL EIGENVALUES OF REVERSIBLE DIFFUSIONS 
IN THE  METASTABLE REGIME

Michael Eckhoff

We investigate the close connection between metastability of the 
reversible
diffusion process X defined by the stochastic differential equation
dX_t=-\nabla F(X_t) dt+\sqrt2\epsilon dW_t,\qquad \epsilon >0, and the 
spectrum
near zero of its generator -L_{\epsilon}\equiv \epsilon \Delta -\nabla
F\cdot\nabla, where F:R^d\to R and W denotes Brownian motion on R^d. For
generic F to each local minimum of F there corresponds a metastable 
state. We
prove that the distribution of its rescaled relaxation time converges 
to the
exponential distribution as \epsilon \downarrow 0 with optimal and 
uniform
error estimates. Each metastable state can be viewed as an eigenstate of
L_{\epsilon} with eigenvalue which converges to zero exponentially fast 
in
1/\epsilon. Modulo errors of exponentially small order in 1/\epsilon 
this
eigenvalue is given as the inverse of the expected metastable 
relaxation time.
The eigenstate is highly concentrated in the basin of attraction of the
corresponding trap.


http://front.math.ucdavis.edu/math.PR/0503600

---------------------------------------------------------------

3275. ASYMPTOTIC EXPANSIONS FOR THE LAPLACE APPROXIMATIONS OF SUMS OF 
BANACH  SPACE-VALUED RANDOM VARIABLES

Sergio Albeverio and Song Liang

Let X_i, i\in N, be i.i.d. B-valued random variables, where B is a real
separable Banach space. Let \Phi be a smooth enough mapping from B into 
R. An
asymptotic evaluation of Z_n=E(\exp (n\Phi (\sum_{i=1}^nX_i/n))), up to 
a
factor (1+o(1)), has been gotten in Bolthausen [Probab. Theory Related 
Fields
72 (1986) 305-318] and Kusuoka and Liang [Probab. Theory Related Fields 
116
(2000) 221-238]. In this paper, a detailed asymptotic expansion of Z_n 
as n\to
\infty is given, valid to all orders, and with control on remainders. 
The
results are new even in finite dimensions.


http://front.math.ucdavis.edu/math.PR/0503601

---------------------------------------------------------------

3276. MULTIPLICATIVE MONOTONE CONVOLUTIONS

Uwe Franz

Recently, Bercovici has introduced multiplicative convolutions based on
Muraki's monotone independence and shown that these convolution of 
probability
measures correspond to the composition of some function of their Cauchy
transforms. We provide a new proof of this fact based on the 
combinatorics of
moments. We also give a new characterisation of the probability 
measures that
can be embedded into continuous monotone convolution semigroups of 
probability
measures on the unit circle and briefly discuss a relation to 
Galton-Watson
processes.


http://front.math.ucdavis.edu/math.PR/0503602

---------------------------------------------------------------

3277. EXTREMES ON TREES

Tailen Hsing and Holger Rootzen

This paper considers the asymptotic distribution of the longest edge of 
the
minimal spanning tree and nearest neighbor graph on X_1,...,X_{N_n} 
where
X_1,X_2,... are i.i.d. in \Re^2 with distribution F and N_n is 
independent of
the X_i and satisfies N_n/n\to_p1. A new approach based on spatial 
blocking and
a locally orthogonal coordinate system is developed to treat cases for 
which F
has unbounded support. The general results are applied to a number of 
special
cases, including elliptically contoured distributions, distributions 
with
independent Weibull-like margins and distributions with parallel level 
curves.


http://front.math.ucdavis.edu/math.PR/0503603

---------------------------------------------------------------

3278. ON THE MONOTONICITY OF THE SPEED OF RANDOM WALKS ON A PERCOLATION 
  CLUSTER OF TREES

Dayue Chen and Fuxi Zhang

We consider the simple random walk on the infinite cluster of the 
Bernoulli
bond percolation of trees, and investigate the relation between the 
speed of
the simple random walk and the retaining probability $p$ by studying 
three
classes of trees. A sufficient condition is established for 
Galton-Watson
trees.


http://front.math.ucdavis.edu/math.PR/0503610

---------------------------------------------------------------

3279. CONTRACTIVE MARKOV SYSTEMS II

Ivan Werner

In this paper, we continue development of the theory of contractive 
Markov
systems (CMSs) initiated in \cite{Wer1}. We extend some results from
\cite{Wer1}, \cite{Wer3}, \cite{Wer5} and \cite{Wer6} to the case of
contractive Markov systems with probabilities which have a square 
summable
variation by using some ideas of A. Johansson and A. Oeberg \cite{JO}. 
In
particular, we show that an irreducible CMS has a unique invariant Borel
probability measure if the vertex sets form an open partition of the 
state
space and the restrictions of the probability functions on their vertex 
sets
have a square summable variation and are bounded away from zero.


http://front.math.ucdavis.edu/math.PR/0503633

---------------------------------------------------------------

3280. LIMIT THEOREMS FOR ITERATED RANDOM TOPICAL OPERATORS

Glenn Merlet (IRMAR)

Let A(n) be a sequence of i.i.d. topical (i.e. isotone and additively
homogeneous) operators. Let $x(n,x\_0)$ be defined by $x(0,x\_0)=x\_0$ 
and
$x(n,x\_0)=A(n)x(n-1,x\_0)$. This can modelize a wide range of systems
including, task graphs, train networks, Job-Shop, timed digital 
circuits or
parallel processing systems. When A(n) has the memory loss property, we 
use the
spectral gap method to prove limit theorems for $x(n,x\_0)$. Roughly 
speaking,
we show that $x(n,x\_0)$ behaves like a sum of i.i.d. real variables.
Precisely, we show that with suitable additional conditions, it 
satisfies a
central limit theorem with rate, a local limit theorem, a renewal 
theorem and a
large deviations principle, and we give an algebraic condition to 
ensure the
positivity of the variance in the CLT. When A(n) are defined by 
matrices in the
\mp semi-ring, we give more effective statements and show that the 
additional
conditions and the positivity of the variance in the CLT are generic.


http://front.math.ucdavis.edu/math.PR/0503634

---------------------------------------------------------------

3281. A PROBABILISTIC APPROACH TO THE GEOMETRY OF THE \ELL_P^N-BALL

Franck Barthe and  Olivier Guedon and  Shahar Mendelson and Assaf Naor

This article investigates, by probabilistic methods, various geometric
questions on B_p^n, the unit ball of \ell_p^n. We propose realizations 
in terms
of independent random variables of several distributions on B_p^n, 
including
the normalized volume measure. These representations allow us to unify 
and
extend the known results of the sub-independence of coordinate slabs in 
B_p^n.
As another application, we compute moments of linear functionals on 
B_p^n,
which gives sharp constants in Khinchine's inequalities on B_p^n and 
determines
the \psi_2-constant of all directions on B_p^n. We also study the 
extremal
values of several Gaussian averages on sections of B_p^n (including 
mean width
and \ell-norm), and derive several monotonicity results as p varies.
Applications to balancing vectors in \ell_2 and to covering numbers of
polyhedra complete the exposition.


http://front.math.ucdavis.edu/math.PR/0503650

---------------------------------------------------------------

3282. MOMENT INEQUALITIES FOR FUNCTIONS OF INDEPENDENT RANDOM VARIABLES

Stephane Boucheron and  Olivier Bousquet and  Gabor Lugosi and Pascal 
Massart

A general method for obtaining moment inequalities for functions of
independent random variables is presented. It is a generalization of the
entropy method which has been used to derive concentration inequalities 
for
such functions [Boucheron, Lugosi and Massart Ann. Probab. 31 (2003)
1583-1614], and is based on a generalized tensorization inequality due 
to
Latala and Oleszkiewicz [Lecture Notes in Math. 1745 (2000) 147-168]. 
The new
inequalities prove to be a versatile tool in a wide range of 
applications. We
illustrate the power of the method by showing how it can be used to
effortlessly re-derive classical inequalities including Rosenthal and
Kahane-Khinchine-type inequalities for sums of independent random 
variables,
moment inequalities for suprema of empirical processes and moment 
inequalities
for Rademacher chaos and U-statistics. Some of these corollaries are 
apparently
new. In particular, we generalize Talagrand's exponential inequality for
Rademacher chaos of order 2 to any order. We also discuss applications 
for
other complex functions of independent random variables, such as 
suprema of
Boolean polynomials which include, as special cases, subgraph counting 
problems
in random graphs.


http://front.math.ucdavis.edu/math.PR/0503651

---------------------------------------------------------------

3283. ON THE STOCHASTIC CALCULUS METHOD FOR SPINS SYSTEMS

Samy Tindel

In this note we show how to generalize the stochastic calculus method
introduced by Comets and Neveu [Comm. Math. Phys. 166 (1995) 549-564] 
for two
models of spin glasses, namely, the SK model with external field and the
perceptron model. This method allows to derive quite easily some 
fluctuation
results for the free energy in those two cases.


http://front.math.ucdavis.edu/math.PR/0503652

---------------------------------------------------------------

3284. CLOSURES OF EXPONENTIAL FAMILIES

Imre Csiszar and Frantisek Matus

The variation distance closure of an exponential family with a convex 
set of
canonical parameters is described, assuming no regularity conditions. 
The tools
are the concepts of convex core of a measure and extension of an 
exponential
family, introduced previously by the authors, and a new concept of 
accessible
faces of a convex set. Two other closures related to the information 
divergence
are also characterized.


http://front.math.ucdavis.edu/math.PR/0503653

---------------------------------------------------------------

3285. ONE-DEPENDENT TRIGONOMETRIC DETERMINANTAL PROCESSES ARE  
TWO-BLOCK-FACTORS

Erik I. Broman

Given a trigonometric polynomial f:[0,1]\to[0,1] of degree m, one can 
define
a corresponding stationary process {X_i}_{i\in Z} via determinants of 
the
Toeplitz matrix for f. We show that for m=1 this process, which is 
trivially
one-dependent, is a two-block-factor.


http://front.math.ucdavis.edu/math.PR/0503654

---------------------------------------------------------------

3286. ASYMPTOTICS FOR HITTING TIMES

M. Kupsa and Y. Lacroix

In this paper we characterize possible asymptotics for hitting times in
aperiodic ergodic dynamical systems: asymptotics are proved to be the
distribution functions of subprobability measures on the line belonging 
to the
functional class {6pt} {-3mm}(A){6mm}F={F:R\to [0,1]:\left\lbrack 
\matrixF is
increasing, null on ]-\infty, 0]; \noalignF is continuous and concave;
\noalignF(t)\le t for t\ge 0.\right.}. {6pt} Note that all possible 
asymptotics
are absolutely continuous.


http://front.math.ucdavis.edu/math.PR/0503655

---------------------------------------------------------------

3287. KREIN'S SPECTRAL THEORY AND THE PALEY-WIENER EXPANSION FOR 
FRACTIONAL  BROWNIAN MOTION

Kacha Dzhaparidze and Harry van Zanten

In this paper we develop the spectral theory of the fractional Brownian
motion (fBm) using the ideas of Krein's work on continuous analogous of
orthogonal polynomials on the unit circle. We exhibit the functions 
which are
orthogonal with respect to the spectral measure of the fBm and obtain an
explicit reproducing kernel in the frequency domain. We use these 
results to
derive an extension of the classical Paley-Wiener expansion of the 
ordinary
Brownian motion to the fractional case.


http://front.math.ucdavis.edu/math.PR/0503656

---------------------------------------------------------------

3288. CRITICALITY FOR BRANCHING PROCESSES IN RANDOM ENVIRONMENT

V. I. Afanasyev and  J. Geiger and  G. Kersting and V. A. Vatutin

We study branching processes in an i.i.d. random environment, where the
associated random walk is of the oscillating type. This class of 
processes
generalizes the classical notion of criticality. The main properties of 
such
branching processes are developed under a general assumption, known as
Spitzer's condition in fluctuation theory of random walks, and some 
additional
moment condition. We determine the exact asymptotic behavior of the 
survival
probability and prove conditional functional limit theorems for the 
generation
size process and the associated random walk. The results rely on a 
stimulating
interplay between branching process theory and fluctuation theory of 
random
walks.


http://front.math.ucdavis.edu/math.PR/0503657

---------------------------------------------------------------

3289. EXAMPLES OF MODERATE DEVIATION PRINCIPLE FOR DIFFUSION PROCESSES

A. Guillin} and  R. Liptser

Taking into account some likeness of moderate deviations (MD) and 
central
limit theorems (CLT), we develop an approach, which made a good showing 
in CLT,
for MD analysis of a family $$ 
S^\kappa_t=\frac{1}{t^\kappa}\int_0^tH(X_s)ds, \
t\to\infty $$ for an ergodic diffusion process $X_t$ under 
$0.5<\kappa<1$ and
appropriate $H$. We mean a decomposition with ``corrector'': $$
\frac{1}{t^\kappa}\int_0^tH(X_s)ds={\rm
corrector}+\frac{1}{t^\kappa}\underbrace{M_t}_{\rm martingale}. $$ and 
show
that, as in the CLT analysis, the corrector is negligible but in the MD 
scale,
and the main contribution in the MD brings the family ``$
\frac{1}{t^\kappa}M_t, t\to\infty. $'' Starting from Bayer and Freidlin,
\cite{BF}, and finishing by Wu's papers \cite{Wu1}-\cite{WuH}, in the 
MD study
Laplace's transform dominates. In the paper, we replace the Laplace 
technique
by one, admitting to give the conditions, providing the MD, in terms of
``drift-diffusion'' parameters and $H$. However, a verification of these
conditions heavily depends on a specificity of a diffusion model. That 
is why
the paper is named ``Examples ...''.


http://front.math.ucdavis.edu/math.PR/0503070

---------------------------------------------------------------

3290. CONFIDENCE INTERVALS FOR NONHOMOGENEOUS BRANCHING PROCESSES AND  
POLYMERASE CHAIN REACTIONS

Didier Piau

We extend in two directions our previous results about the sampling and 
the
empirical measures of immortal branching Markov processes. Direct 
applications
to molecular biology are rigorous estimates of the mutation rates of 
polymerase
chain reactions from uniform samples of the population after the 
reaction.
First, we consider nonhomogeneous processes, which are more adapted to 
real
reactions. Second, recalling that the first moment estimator is 
analytically
known only in the infinite population limit, we provide rigorous 
confidence
intervals for this estimator that are valid for any finite population. 
Our
bounds are explicit, nonasymptotic and valid for a wide class of 
nonhomogeneous
branching Markov processes that we describe in detail. In the setting of
polymerase chain reactions, our results imply that enlarging the size 
of the
sample becomes useless for surprisingly small sizes. Establishing 
confidence
intervals requires precise estimates of the second moment of random 
samples.
The proof of these estimates is more involved than the proofs that 
allowed us,
in a previous paper, to deal with the first moment. On the other hand, 
our
method uses various, seemingly new, monotonicity properties of the 
harmonic
moments of sums of exchangeable random variables.


http://front.math.ucdavis.edu/math.PR/0503659

---------------------------------------------------------------

3291. SECTORIAL CONVERGENCE OF U-STATISTICS

Anda Gadidov

In this note we show that almost sure convergence to zero of symmetrized
U-statistics indexed by a linear sector in Z^d_+ is equivalent to 
convergence
along the diagonal of Z^d_+, as it is considered in Lata\la and Zinn 
[Ann.
Probab. 28 (2000) 1908-1924]. Comparisons with similar results for sums 
of
multi-indexed i.i.d. random variables are also made.


http://front.math.ucdavis.edu/math.PR/0503660

---------------------------------------------------------------

3292. A STRONG INVARIANCE PRINCIPLE FOR ASSOCIATED RANDOM FIELDS

Raluca M. Balan

In this paper we generalize Yu's [Ann. Probab. 24 (1996) 2079-2097] 
strong
invariance principle for associated sequences to the multi-parameter 
case,
under the assumption that the covariance coefficient u(n) decays 
exponentially
as n\to \infty. The main tools that we use are the following: the 
Berkes and
Morrow [Z. Wahrsch. Verw. Gebiete 57 (1981) 15-37] multi-parameter 
blocking
technique, the Csorgo and Revesz [Z. Wahrsch. Verw. Gebiete 31 (1975) 
255-260]
quantile transform method and the Bulinski [Theory Probab. Appl. 40 
(1995)
136-144] rate of convergence in the CLT.


http://front.math.ucdavis.edu/math.PR/0503661

---------------------------------------------------------------

3293. MODERATE DEVIATION PRINCIPLE FOR ERGODIC MARKOV CHAIN. LIPSCHITZ  
SUMMANDS

B. Delyon and  A. Juditsky and  R. Liptser

For ${1/2}<\alpha<1$, we propose the MDP analysis for family $$
S^\alpha_n=\frac{1}{n^\alpha}\sum_{i=1}^nH(X_{i-1}), n\ge 1, $$ where
$(X_n)_{n\ge 0}$ be a homogeneous ergodic Markov chain, $X_n\in 
\mathbb{R}^d$,
when the spectrum of operator $P_x$ is continuous. The vector-valued 
function
$H$ is not assumed to be bounded but the Lipschitz continuity of $H$ is
required. The main helpful tools in our approach are Poisson's equation 
and
Stochastic Exponential; the first enables to replace the original 
family by
$\frac{1}{n^\alpha}M_n$ with a martingale $M_n$ while the second to 
avoid the
direct Laplace transform analysis.


http://front.math.ucdavis.edu/math.PR/0503071

---------------------------------------------------------------

3294. DISTANCES IN RANDOM GRAPHS WITH FINITE MEAN AND INFINITE VARIANCE 
  DEGREES

Remco van der Hofstad and  Gerard Hooghiemstra and  Dmitri Znamenski

In this paper we study random graphs with independent and identically
distributed degrees of which the tail of the distribution function is 
regularly
varying with exponent $\tau\in (2,3)$.
   The number of edges between two arbitrary nodes, also called the graph
distance or hopcount, in a graph with $N$ nodes is investigated when 
$N\to
\infty$. When $\tau\in (2,3)$, this graph distance grows like 
$2\frac{\log\log
N}{|\log(\tau-2)|}$. In different papers, the cases $\tau>3$ and 
$\tau\in
(1,2)$ have been studied. We also study the fluctuations around these
asymptotic means, and describe their distributions. The results 
presented here
improve upon results of Reittu and Norros, who prove an upper bound 
only.


http://front.math.ucdavis.edu/math.PR/0502581

---------------------------------------------------------------

3295. ON TAIL DISTRIBUTIONS OF SUPREMUM AND QUADRATIC VARIATION OF 
LOCAL  MARTINGALES

R. Liptser and  A. Novikov

We extend some known results relating the distribution tails of a 
continuous
local martingale supremum and its quadratic variation to the case of 
locally
square integrable martingales with bounded jumps. The predictable and 
optional
quadratic variations are involved in the main result.


http://front.math.ucdavis.edu/math.PR/0503072

---------------------------------------------------------------

3296. LIMIT THEOREMS FOR BIPOWER VARIATION IN FINANCIAL ECONOMETRICS

Ole E. Barndorff-Nielsen (DEPT Math Sci) and  Svend E. Graversen (DEPT  
Math Sci), Jean Jacod (PMA), Neil Shephard (NUFFIELD College)

In this paper we provide an asymptotic analysis of generalised bipower
measures of the variation of price processes in financial economics. 
These
measures encompass the usual quadratic variation, power variation and 
bipower
variations which have been highlighted in recent years in financial
econometrics. The analysis is carried out under some rather general 
Brownian
semimartingale assumptions, which allow for standard leverage effects.


http://front.math.ucdavis.edu/math.PR/0503711

---------------------------------------------------------------

3297. RANDOM WALKS IN A DIRICHLET ENVIRONMENT

Nathana\"el Enriquez and  Christophe Sabot

This paper states a law of large numbers for a random walk in a random 
iid
environment on ${\mathbb Z}^d$, where the environment follows some 
Dirichlet
distribution. Moreover, we give explicit bounds for the asymptotic 
velocity of
the process and also an asymptotic expansion of this velocity at low 
disorder.


http://front.math.ucdavis.edu/math.PR/0503713

---------------------------------------------------------------

3298. RANDOM WALKS IN A RANDOM ENVIRONMENT

S R S Varadhan

Random walks as well as diffusions in random media are considered. 
Methods
are developed that allow one to establish large deviation results for 
both the
`quenched' and the `averaged' case.


http://front.math.ucdavis.edu/math.PR/0503089

---------------------------------------------------------------

3299. RANDOM TREES AND GENERAL BRANCHING PROCESSES

Anna Rudas and  Balint Toth and  Benedek Valko

We consider a model of random tree growth, where at each time unit a new
vertex is added and attached to an already existing vertex chosen at 
random.
The probability with which a vertex with degree $k$ is chosen is 
proportional
to $w(k)$, where the weight function $w$ is the parameter of the model.
   In the papers of B. Bollobas, O. Riordan, J. Spencer, G. Tusnady, and,
independently, Mori, the asymptotic degree distribution is obtained for 
a model
that is equivalent to the special case of ours, when the weight 
function is
linear. The proof therein strongly relies on the linear choice of $w$.
   We give the asymptotical degree distribution for a wide range of 
weight
functions. Moreover, we provide the asymptotic distribution of the tree 
itself
as seen from a randomly selected vertex. The latter approach is new and 
gives
full insight to the limiting structure of the tree.
   Our proof relies on the fact that considering the evolution of the 
random
tree in continuous time, the process may be viewed as a general 
branching
process, this way classical results can be applied.


http://front.math.ucdavis.edu/math.PR/0503728

---------------------------------------------------------------

3300. MIXED POISSON APPROXIMATION OF NODE DEPTH DISTRIBUTIONS IN RANDOM 
BINARY  SEARCH TREES

Rudolf Grubel and Nikolce Stefanoski

We investigate the distribution of the depth of a node containing a 
specific
key or, equivalently, the number of steps needed to retrieve an item 
stored in
a randomly grown binary search tree. Using a representation in terms of 
mixed
and compounded standard distributions, we derive approximations by 
Poisson and
mixed Poisson distributions; these lead to asymptotic normality 
results. We are
particularly interested in the influence of the key value on the 
distribution
of the node depth. Methodologically our message is that the explicit
representation may provide additional insight if compared to the 
standard
approach that is based on the recursive structure of the trees. 
Further, in
order to exhibit the influence of the key on the distributional 
asymptotics, a
suitable choice of distance of probability distributions is important. 
Our
results are also applicable in connection with the number of recursions 
needed
in Hoare's [Comm. ACM 4 (1961) 321-322] selection algorithm Find.


http://front.math.ucdavis.edu/math.PR/0503738

---------------------------------------------------------------

3301. ON FRACTIONAL TEMPERED STABLE MOTION

C. Houdr\'e and  R. Kawai

Fractional tempered stable motion (fTSm)} is defined and studied. FTSm 
has
the same covariance structure as fractional Brownian motion, while 
having tails
heavier than Gaussian but lighter than stable. Moreover, in short time 
it is
close to fractional stable L\'evy motion, while it is approximately 
fractional
Brownian motion in long time. A series representation of fTSm is 
derived and
used for simulation and to study some of its sample path properties.


http://front.math.ucdavis.edu/math.PR/0503741

---------------------------------------------------------------

3302. ON LAYERED STABLE PROCESSES

C. Houdr\'e and  R. Kawai

Layered stable (multivariate) distributions and processes are defined 
and
studied. A layered stable process combines stable trends of two 
different
indices, one of them possibly Gaussian. More precisely, in short time, 
it is
close to a stable process while, in long time, it approximates another 
stable
(possibly Gaussian) process. We also investigate the absolute 
continuity of a
layered stable process with respect to its short time limiting stable 
process.
A series representation of layered stable processes is derived, giving 
insights
into both the structure of the sample paths and of the short and long 
time
behaviors. This series is further used for sample paths simulation.


http://front.math.ucdavis.edu/math.PR/0503742

---------------------------------------------------------------

3303. MEASURE FREE MARTINGALES

Rajeeva L Karandikar and M G Nadkarni

We give a necessary and sufficient condition on a sequence of functions 
on a
set $\Omega$ under which there is a measure on $\Omega$ which renders 
the given
sequence of functions a martingale. Further such a measure is unique if 
we
impose a natural maximum entropy condition on the conditional 
probabilities.


http://front.math.ucdavis.edu/math.PR/0503099

---------------------------------------------------------------

3304. METRIC STABILITY FOR RANDOM WALKS (WITH APPLICATIONS IN 
RENORMALIZATION  THEORY)

Carlos G. Moreira (IMPA-Brazil) Daniel Smania (ICMC-USP-Brazil)

Consider deterministic random walks F: I x Z -> I x Z, defined by
F(x,n)=(f(x), K(x)+n), where f is an expanding Markov map on the 
interval I and
K: I->Z. We study the universality (stability) of ergodic (for instance,
recurrence and transience), geometric and multifractal properties in 
the class
of perturbations of the type G(x,n)=(f_n(x), L(x,n)+n) which are 
topologically
conjugate with F and f_n are expanding maps exponentially close to f 
when |n|
goes to infinity. We give applications of these results in the study of 
the
regularity of conjugacies between (generalized) infinitely 
renormalizable maps
of the interval and the existence of wild attractors for 
one-dimensional maps.


http://front.math.ucdavis.edu/math.DS/0503736

---------------------------------------------------------------

3305. THE JAMMED PHASE OF THE BIHAM-MIDDLETON-LEVINE TRAFFIC MODEL

Omer Angel and  Alexander E Holroyd and James B Martin

Initially a car is placed with probability p at each site of the
two-dimensional integer lattice. Each car is equally likely to be 
East-facing
or North-facing, and different sites receive independent assignments. 
At odd
time steps, each North-facing car moves one unit North if there is a 
vacant
site for it to move into. At even time steps, East-facing cars move 
East in the
same way. We prove that when p is sufficiently close to 1 traffic is 
jammed, in
the sense that no car moves infinitely many times. The result extends to
several variant settings, including a model with cars moving at random 
times,
and higher dimensions.


http://front.math.ucdavis.edu/math.PR/0504001

---------------------------------------------------------------

3306. BSDE WITH QUADRATIC GROWTH AND UNBOUNDED TERMINAL VALUE

Philippe Briand (IRMAR) and  Ying Hu (IRMAR)

In this paper, we study the existence of solution to BSDE with quadratic
growth and unbounded terminal value. We apply a localization procedure 
together
with a priori bounds. As a byproduct, we apply the same method to 
extend a
result on BSDEs with integrable terminal condition.


http://front.math.ucdavis.edu/math.PR/0504002

---------------------------------------------------------------

3307. THE HEAT EQUATION WITH MULTIPLICATIVE STABLE L\'EVY NOISE

Carl Mueller and Leonid Mytnik and Aurel Stan

We study the heat equation with a random potential term. The potential 
is a
one-sided stable noise, with positive jumps, which does not depend on 
time. To
avoid singularities, we define the equation in terms of a construction 
similar
to the Skorokhod integral or Wick product. We give a criterion for 
existence
based on the dimension of the space variable, and the parameter p of 
the stable
noise. Our arguments are different for p<1 and p>1.


http://front.math.ucdavis.edu/math.PR/0504027

---------------------------------------------------------------

3308. THE FULL SCALING LIMIT OF TWO-DIMENSIONAL CRITICAL PERCOLATION

Federico Camia and  Charles M. Newman

We use SLE(6) paths to construct a process of continuum nonsimple loops 
in
the plane and prove that this process coincides with the full continuum 
scaling
limit of 2D critical site percolation on the triangular lattice -- that 
is, the
scaling limit of the set of all interfaces between different clusters. 
Some
properties of the loop process, including conformal invariance, are also
proved. In the main body of the paper these results are proved while 
assuming,
as argued by Schramm and Smirnov, that the percolation exploration path
converges in distribution to the trace of chordal SLE(6). Then, in a 
lengthy
appendix, a detailed proof is provided for this convergence to SLE(6), 
which
itself relies on Smirnov's result that crossing probabilities converge 
to
Cardy's formula.


http://front.math.ucdavis.edu/math.PR/0504036

---------------------------------------------------------------

3309. MINIMAX AND ADAPTIVE ESTIMATION OF THE WIGNER FUNCTION IN QUANTUM 
  HOMODYNE TOMOGRAPHY WITH NOISY DATA

Cristina Butucea (PMA and  MODALX) and  Madalin Guta and  Luis Artiles

We estimate the quantum state of a light beam from results of quantum
homodyne measurements performed on identically prepared quantum 
systems. The
state is represented through the Wigner function, a density on R2 which 
may
take negative values but must respect intrinsic positivity constraints 
imposed
by quantum physics. The effect of the losses due to detection 
inefficiencies
which are always present in a real experiment is the addition to the
tomographic data of independent Gaussian noise. We construct a kernel 
estimator
for the Wigner function and prove that it is minimax efficient for the
pointwise risk over a class of infinitely differentiable functions. For 
the L2
risk, we compute the upper bounds of a truncated kernel estimator over 
the same
classes, restricted to functions with sub-Gaussian asymptotic 
behaviour. We
construct adaptive estimators, i.e. which do not depend on the 
smoothness
parameters, and prove that in some set-ups they attain the minimax 
rates for
the corresponding smoothness class.


http://front.math.ucdavis.edu/math.PR/0504058

---------------------------------------------------------------

3310. POINT PROCESS MODEL OF 1/F NOISE VERSUS A SUM OF LORENTZIANS

B. Kaulakys and  V. Gontis and  and M. Alaburda

We present a simple point process model of $1/f^{\beta}$ noise, covering
different values of the exponent $\beta$. The signal of the model 
consists of
pulses or events. The interpulse, interevent, interarrival, recurrence 
or
waiting times of the signal are described by the general Langevin 
equation with
the multiplicative noise and stochastically diffuse in some interval 
resulting
in the power-law distribution. Our model is free from the requirement 
of a wide
distribution of relaxation times and from the power-law forms of the 
pulses. It
contains only one relaxation rate and yields $1/f^ {\beta}$ spectra in 
a wide
range of frequency. We obtain explicit expressions for the power 
spectra and
present numerical illustrations of the model. Further we analyze the 
relation
of the point process model of $1/f$ noise with the 
Bernamont-Surdin-McWhorter
model, representing the signals as a sum of the uncorrelated 
components. We
show that the point process model is complementary to the model based 
on the
sum of signals with a wide-range distribution of the relaxation times. 
In
contrast to the Gaussian distribution of the signal intensity of the 
sum of the
uncorrelated components, the point process exhibits asymptotically a 
power-law
distribution of the signal intensity. The developed multiplicative point
process model of $1/f^{\beta}$ noise may be used for modeling and 
analysis of
stochastic processes in different systems with the power-law 
distribution of
the intensity of pulsing signals.


http://front.math.ucdavis.edu/cond-mat/0504025

---------------------------------------------------------------

3311. A RANDOM WALK PROOF OF THE ERDOS-TAYLOR CONJECTURE

Jay Rosen

For the simple random walk in Z^2 we study those points which are 
visited an
unusually large number of times, and provide a new proof of the 
Erdos-Taylor
conjecture describing the number of visits to the most visited point.


http://front.math.ucdavis.edu/math.PR/0503108

---------------------------------------------------------------

3312. WHAT IS ALWAYS STABLE IN NONLINEAR FILTERING?

P. Chigansky and  R. Liptser

This note addresses certain stability properties of the nonlinear 
filtering
equation in discrete time. The available positive and negative results 
indicate
that much depends on the structure of the signal state space, its 
ergodic
properties and observations regularity. We show that certain predicting
estimates are stable under surprisingly general assumptions.


http://front.math.ucdavis.edu/math.PR/0504094

---------------------------------------------------------------

3313. HOW LIKELY IS AN I.I.D. DEGREE SEQUENCE TO BE GRAPHICAL?

Richard Arratia and Thomas M. Liggett

Given i.i.d. positive integer valued random variables D_1,...,D_n, one 
can
ask whether there is a simple graph on n vertices so that the degrees 
of the
vertices are D_1,...,D_n. We give sufficient conditions on the 
distribution of
D_i for the probability that this be the case to be asymptotically 0, 
{1/2} or
strictly between 0 and {1/2}. These conditions roughly correspond to 
whether
the limit of nP(D_i\geq n) is infinite, zero or strictly positive and 
finite.
This paper is motivated by the problem of modeling large communications
networks by random graphs.


http://front.math.ucdavis.edu/math.PR/0504096

---------------------------------------------------------------

3314. THE UNIVERSALITY CLASSES IN THE PARABOLIC ANDERSON MODEL

Remco van der Hofstad and  Wolfgang Koenig and  Peter Moerters

We discuss the long time behaviour of the parabolic Anderson model, the
Cauchy problem for the heat equation with random potential on $\Z^d$. We
consider general i.i.d. potentials and show that exactly \emph{four}
qualitatively different types of intermittent behaviour can occur. 
These four
universality classes depend on the upper tail of the potential 
distribution:
(1) tails at $\infty$ that are thicker than the double-exponential 
tails, (2)
double-exponential tails at $\infty$ studied by G\"artner and 
Molchanov, (3) a
new class called \emph{almost bounded potentials}, and (4) potentials 
bounded
from above studied by Biskup and K\"onig. The new class (3), which 
contains
both unbounded and bounded potentials, is studied in both the annealed 
and the
quenched setting. We show that intermittency occurs on unboundedly 
increasing
islands whose diameter is slowly varying in time. The characteristic
variational formulas describing the optimal profiles of the potential 
and of
the solution are solved explicitly by parabolas, respectively, Gaussian
densities.


http://front.math.ucdavis.edu/math.PR/0504102

---------------------------------------------------------------

3315. INVARIANCE PRINCIPLES FOR LABELED MOBILES AND BIPARTITE PLANAR 
MAPS

Jean-Fran\c{c}ois Marckert (LM-Versailles) and  Gr\'{e}gory Miermont  
(LM-Orsay)

A class of labeled trees, called mobiles, was introduced by Bouttier-di
Francesco and Guitter in order to generalize the bijective studies of 
planar
maps initiated by Cori-Vauquelin and Schaeffer. We prove an invariance
principle for rescaled random mobiles associated with bipartite random 
planar
maps under a Boltzmann distribution. We infer that the latter converge 
in a
certain sense to the Brownian map introduced by Marckert and Mokkadem, 
which
encompasses results of Chassaing and Schaeffer on quadrangulations 
(although in
a slightly different context). These results are derived from a new 
invariance
principle for a class of two-type Galton-Watson trees coupled with a 
spatial
motion, which are shown to converge to the Brownian snake.


http://front.math.ucdavis.edu/math.PR/0504110

---------------------------------------------------------------

3316. TRACY-WIDOM LIMIT FOR THE LARGEST EIGENVALUE OF A LARGE CLASS OF 
COMPLEX  WISHART MATRICES

Noureddine El Karoui

We study the limiting behavior of the largest eigenvalue of a large 
class of
complex Wishart matrices. In other words, let X be an n*p matrix, and 
let its
rows be i.i.d complex normal N_{C}(0,Sigma_p). We denote by H_p the 
spectral
distribution of Sigma_p, and call lambda_i's its ordered eigenvalues. 
Let us
call l_i's the ordered eigenvalues of X^*X and c the unique root in
[0,1/lambda_1(Sigma_p)) of the equation
   \int ((lambda c)/(1-\lambda c))^2 dH_p(lambda) = n/p. The main result 
of this
paper is that, under technical conditions on (Sigma_p,n,p), we have, 
when
n->\infty,
   (l_1(X^*X)-n mu)/(n^{1/3} sigma) -> TW_2 .
  We give explicit formulas for mu and sigma, that depend non trivially 
on c.
Here TW_2 denotes the Tracy-Widom law appearing in the study of the 
Gaussian
Unitary Ensemble.
   This theorem applies to a number of covariance models found in 
applications,
including well-behaved Toeplitz matrices and covariance matrices whose 
spectral
distribution is a sum of atoms (under some conditions on the mass of the
atoms). Generalizations of the theorem to certain spiked versions of 
models in
G and a.s statements about l_1/n are given. Most known examples of 
convergence
of the largest eigenvalue of a complex sample covariance matrix to this
Tracy-Widom law are subcases of this result.


http://front.math.ucdavis.edu/math.PR/0503109

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3317. DETERMINANTAL PROCESSES AND INDEPENDENCE

J. Ben Hough and  Manjunath Krishnapur and  Yuval Peres and Balint Virag

We give a probabilistic introduction to determinantal and permanental 
point
processes. Determinantal processes arise in physics (fermions, 
eigenvalues of
random matrices) and in combinatorics (nonintersecting paths, random 
spanning
trees). They have the striking property that the number of points in a 
region
$D$ is a sum of independent Bernoulli random variables, with parameters 
which
are eigenvalues of the relevant operator on $L^2(D)$. Moreover, any
determinantal process can be represented as a mixture of determinantal
projection processes. We give a simple explanation for these known 
facts, and
establish analogous representations for permanental processes, with 
geometric
variables replacing the Bernoulli variables. These representations lead 
to
simple proofs of existence criteria and central limit theorems, and 
unify known
results on the distribution of absolute values in certain processes with
radially symmetric distributions.


http://front.math.ucdavis.edu/math.PR/0503110

---------------------------------------------------------------

3318. RANDOM WALK ON THE INCIPIENT INFINITE CLUSTER ON TREES

Martin T. Barlow and Takashi Kumagai

Let ${\cal G}$ be the incipient infinite cluster (IIC) for percolation 
on a
homogeneous tree of degree $n_0+1$. We obtain estimates for the 
transition
density of the continuous time simple random walk $Y$ on ${\cal G}$; the
process satisfies anomalous diffusion and has spectral dimension 4/3.


http://front.math.ucdavis.edu/math.PR/0503118

---------------------------------------------------------------

3319. QUANTITATIVE CONCENTRATION INEQUALITIES FOR EMPIRICAL MEASURES ON 
  NON-COMPACT SPACES

Francois Bolley and  Arnaud Guillin and  Cedric Villani

We establish some quantitative concentration estimates for the empirical
measure of many independent variables, in transportation distances. As 
an
application, we provide some error bounds for particle simulations in a 
model
mean field problem. The tools include coupling arguments, as well as 
regularity
and moments estimates for solutions of certain diffusive partial 
differential
equations.


http://front.math.ucdavis.edu/math.PR/0503123

---------------------------------------------------------------

3320. ON THE BIAS OF TRACEROUTE SAMPLING; OR, POWER-LAW DEGREE 
DISTRIBUTIONS  IN REGULAR GRAPHS

Dimitris Achlioptas and  Aaron Clauset and  David Kempe and  and 
Cristopher Moore

Understanding the structure of the Internet graph is a crucial step for
building accurate network models and designing efficient algorithms for
Internet applications. Yet, obtaining its graph structure is a 
surprisingly
difficult task, as edges cannot be explicitly queried. Instead, 
empirical
studies rely on traceroutes to build what are essentially single-source,
all-destinations, shortest-path trees. These trees only sample a 
fraction of
the network's edges, and a recent paper by Lakhina et al. found 
empirically
that the resuting sample is intrinsically biased. For instance, the 
observed
degree distribution under traceroute sampling exhibits a power law even 
when
the underlying degree distribution is Poisson.
   In this paper, we study the bias of traceroute sampling 
systematically, and,
for a very general class of underlying degree distributions, calculate 
the
likely observed distributions explicitly. To do this, we use a 
continuous-time
realization of the process of exposing the BFS tree of a random graph 
with a
given degree distribution, calculate the expected degree distribution 
of the
tree, and show that it is sharply concentrated. As example applications 
of our
machinery, we show how traceroute sampling finds power-law degree 
distributions
in both delta-regular and Poisson-distributed random graphs. Thus, our 
work
puts the observations of Lakhina et al. on a rigorous footing, and 
extends them
to nearly arbitrary degree distributions.


http://front.math.ucdavis.edu/cond-mat/0503087

---------------------------------------------------------------

3321. THE CRITICAL ISING MODEL ON TREES, CONCAVE RECURSIONS AND 
NONLINEAR  CAPACITY

Robin Pemantle and Yuval Peres

We consider the Ising model on a general tree under various boundary
conditions: all plus, free and spin-glass. In each case, we determine 
when the
root is influenced by the boundary values in the limit as the boundary 
recedes
to infinity. We obtain exact capacity criteria that govern behavior at 
critical
temperatures. For plus boundary conditions, an $L^3$ capacity arises. In
particular, on a spherically symmetric tree that has $n^c b^n$ vertices 
at
level $n$ (up to bounded factors), we prove that there is a unique Gibbs
measure for the ferromagnetic Ising model if and only if $c$ is at most 
1/2.
Our proofs are based on a new link between nonlinear recursions on 
trees and
$L^p$ capacities.


http://front.math.ucdavis.edu/math.PR/0503137

---------------------------------------------------------------

3322. HOW LARGE A DISC IS COVERED BY A RANDOM WALK IN $N$ STEPS?

Amir Dembo and  Yuval Peres and Jay Rosen

We show that the largest disc covered by a simple random walk on the 
planar
square lattice after $n$ steps has radius $n^{1/4+o(1)}$, thus 
resolving an
open problem of P. R\'ev\'esz (1990). We also show that almost surely, 
for
infinitely many values of $n$ it takes about $n^{1/2+o(1)}$ steps after 
step
$n$ for the random walk to reach the first previously unvisited site 
(and the
exponent 1/2 is sharp). This resolves a problem raised by P. R\'ev\'esz 
(1993).
Additional results on multiple covering are obtained as well.


http://front.math.ucdavis.edu/math.PR/0503139

---------------------------------------------------------------

3323. INFINITE DIMENSIONAL STOCHASTIC DIFFERENTIAL EQUATIONS OF  
ORNSTEIN-UHLENBECK TYPE

Siva R. Athreya and  Richard F. Bass and  Maria Gordina and  Edwin A. 
Perkins

We consider the operator $$\sL f(x)=\tfrac12 \sum_{i,j=1}^\infty
a_{ij}(x)\frac{\del^2 f}{\del x_i \del x_j}(x)-\sum_{i=1}^\infty \lam_i 
x_i
b_i(x) \frac{\del f}{\del x_i}(x).$$ We prove existence and uniqueness 
of
solutions to the martingale problem for this operator under appropriate
conditions on the $a_{ij}, b_i$, and $\lam_i$. The process 
corresponding to
$\sL$ solves an infinite dimensional stochastic differential equation 
similar
to that for the infinite dimensional Ornstein-Uhlenbeck process.


http://front.math.ucdavis.edu/math.PR/0503165

---------------------------------------------------------------

3324. ON CHORDAL AND BILATERAL SLE IN MULTIPLY CONNECTED DOMAINS

Robert O. Bauer and  Roland M. Friedrich

We discuss the possible candidates for conformally invariant random
non-self-crossing curves which begin and end on the boundary of a 
multiply
connected planar domain, and which satisfy a Markovian-type property. We
consider both, the case when the curve connects a boundary component to 
itself
(chordal), and the case when the curve connects two different boundary
components (bilateral). We establish appropriate extensions of Loewner's
equation to multiply connected domains for the two cases. We show that 
a curve
in the domain induces a motion on the boundary and that this motion is 
enough
to first recover the motion of the moduli of the domain and then, 
second, the
curve in the interior. For random curves in the interior we show that 
the
induced random motion on the boundary is not Markov if the domain is 
multiply
connected, but that the random motion on the boundary together with the 
random
motion of the moduli forms a Markov process. In the chordal case, we 
show that
this Markov process satisfies Brownian scaling and discuss how this 
limits the
possible conformally invariant random non-self-crossing curves. We show 
that
the possible candidates are labeled by a real constant and a function
homogeneous of degree minus one which describes the interaction of the 
random
curve with the boundary. We show that the random curve has the locality
property if the interaction term vanishes and the real parameter equals 
six.


http://front.math.ucdavis.edu/math.PR/0503178

---------------------------------------------------------------

3325. FROM N-PARAMETER FRACTIONAL BROWNIAN MOTIONS TO N-PARAMETER  
MULTIFRACTIONAL BROWNIAN MOTIONS

E. Herbin

Multifractional Brownian motion is an extension of the well-known 
fractional
Brownian motion where the Holder regularity is allowed to vary along 
the paths.
In this paper, two kind of multi-parameter extensions of mBm are 
studied: one
is isotropic while the other is not. For each of these processes, a 
moving
average representation, a harmonizable representation, and the 
covariance
structure are given. The Holder regularity is then studied. In 
particular, the
case of an irregular exponent function H is investigated. In this 
situation,
the almost sure pointwise and local Holder exponents of the 
multi-parameter mBm
are proved to be equal to the correspondent exponents of H. Eventually, 
a local
asymptotic self-similarity property is proved. The limit process can be 
another
process than fBm.


http://front.math.ucdavis.edu/math.PR/0503182

---------------------------------------------------------------

3326. EXAMPLES OF GROUPS THAT ARE MEASURE EQUIVALENT TO THE FREE GROUP

Damien Gaboriau (UMPA-ENSL)

Measure Equivalence (ME) is the measure theoretic counterpart of
quasi-isometry. This field grew considerably during the last years, 
developing
tools to distinguish between different ME classes of countable groups. 
On the
other hand, contructions of ME equivalent groups are very rare. We 
present a
new method, based on a notion of measurable free-factor, and we apply 
it to
exhibit a new family of groups that are measure equivalent to the free 
group.
We also present a quite extensive survey on results about Measure 
Equivalence
for countable groups.


http://front.math.ucdavis.edu/math.DS/0503181

---------------------------------------------------------------

3327. ORTHOGONAL POLYNOMIALS AND FLUCTUATIONS OF RANDOM MATRICES

Timothy Kusalik and  James A. Mingo and  and Roland Speicher

In this paper we establish a connection between the fluctuations of 
Wishart
random matrices, shifted Chebyshev polynomials, and planar diagrams 
whose
linear span form a basis for the irreducible representations of the 
annular
Temperly-Lieb algebra.


http://front.math.ucdavis.edu/math.OA/0503169

---------------------------------------------------------------

3328. COUNTING CONNECTED GRAPHS ASYMPTOTICALLY

Remco van der Hofstad and  Joel Spencer

We find the asymptotic number of connected graphs with $k$ vertices and
$k-1+l$ edges when $k,l$ approach infinity, reproving a result of 
Bender,
Canfield and McKay. We use the {\em probabilistic method}, analyzing
breadth-first search on the random graph $G(k,p)$ for an appropriate 
edge
probability $p$. Central is analysis of a random walk with fixed 
beginning and
end which is tilted to the left.


http://front.math.ucdavis.edu/math.CO/0502579

---------------------------------------------------------------

3329. ON Q-FUNCTIONAL EQUATIONS AND EXCURSION MOMENTS

Christoph Richard

We analyse q-functional equations arising from tree-like combinatorial
structures, which are counted by size, internal path length and certain
generalisations thereof. The corresponding counting parameters are 
labelled by
an integer k>1. We show the existence of a joint limit distribution for 
these
parameters in the limit of infinite size, if the size generating 
function has a
square root as dominant singularity. The limit distribution coincides 
with that
of integrals of (k-1)th powers of the standard Brownian excursion. Our 
method
yields a recursion for the moments of the joint distribution and admits 
an
extension to other types of singularities.


http://front.math.ucdavis.edu/math.CO/0503198

---------------------------------------------------------------

3330. A SET-INDEXED FRACTIONAL BROWNIAN MOTION

E. Herbin and E. Merzbach

We define and prove the existence of a fractional Brownian motion 
indexed by
a collection of closed subsets of a measure space. This process is a
generalization of the set-indexed Brownian motion, when the condition of
independance is relaxed. Relations with the Levy fractional Brownian 
motion and
with the fractional Brownian sheet are studied. We prove stationarity 
of the
increments and a property of self-similarity with respect to the action 
of
solid motions. Regularity conditions are exhibited. Finally, behavior 
of the
set-indexed fractional Brownian motion along increasing paths is 
analysed.


http://front.math.ucdavis.edu/math.PR/0503211

---------------------------------------------------------------

3331. ENTROPY-DRIVEN PHASE TRANSITION IN A POLYDISPERSE HARD-RODS 
LATTICE  SYSTEM

Dmitry Ioffe and  Yvan Velenik (LMRS) and  Milos Zahradnik

We study a system of rods on the 2d square lattice, with hard-core 
exclusion.
Each rod has a length between 2 and N. We show that, when N is 
sufficiently
large, and for suitable fugacity, there are several distinct Gibbs 
states, with
orientational long-range order. This is in sharp contrast with the case 
N=2
(the monomer-dimer model), for which Heilmann and Lieb proved absence 
of phase
transition at any fugacity. This is the first example of a pure 
hard-core
system with phases displaying orientational order, but not 
translational order;
this is a fundamental characteristic feature of liquid crystals.


http://front.math.ucdavis.edu/math.PR/0503222

---------------------------------------------------------------

3332. AN INDUCTIVE PROOF OF THE BERRY-ESSEEN THEOREM FOR CHARACTER 
RATIOS

Jason Fulman

Bolthausen used a variation of Stein's method to give an inductive 
proof of
the Berry-Esseen theorem for sums of independent, identically 
distributed
random variables. We modify this technique to prove a Berry-Esseen 
theorem for
character ratios of a random representation of the symmetric group on
transpositions. An analogous result is proved for Jack measure on 
partitions.


http://front.math.ucdavis.edu/math.CO/0503227

---------------------------------------------------------------

3333. MAX-SEMI-SELFDECOMPOSABLE LAWS AND RELATED PROCESSES

S Satheesh and E Sandhya

Methods of construction of Max-semi-selfdecompsable laws are given.
Implications of this method in random time changed extremal processes 
are
discussed. Max-autoregressive model is introduced and characterized 
using the
max-semi-selfdecompsable laws and exponential max-semi-stable laws. Some
comments regarding the infinite divisibility of semi-stable and 
max-semi-stable
laws are given.


http://front.math.ucdavis.edu/math.PR/0503232

---------------------------------------------------------------

3334. DISCRETE INTERPOLATION BETWEEN MONOTONE PROBABILITY AND FREE 
PROBABILITY

Romuald Lenczewski and  Rafal Salapata

We construct a sequence of states called m-monotone product states 
which give
a discrete interpolation between the monotone product of states of 
Muraki and
the free product of states of Avitzour and Voiculescu in free 
probability. We
derive the associated basic limit theorems and develop the 
combinatorics based
on non-crossing ordered partitions with monotone order starting from 
depth m.
The Hilbert space representations of the limit mixed moments in the 
invariance
principle lead to m-monotone Gaussian operators living in m-monotone 
Fock
spaces, which are truncations of the free Fock space over the 
square-integrable
functions on the non-negative real line (m=1 gives the monotone Fock 
space). A
new type of combinatorics of inner blocks leads to explicit formulas 
for the
mixed moments of m-monotone Gaussian operators, which are new even in 
the case
of monotone independent Gaussian operators with arcsine distributions.


http://front.math.ucdavis.edu/math.QA/0502570

---------------------------------------------------------------

3335. RIFFLE SHUFFLES OF DECKS WITH REPEATED CARDS

Mark Conger and D. Viswanath

By a well-known result of Bayer and Diaconis, the maximum entropy model 
of
the common riffle shuffle implies that the number of riffle shuffles 
necessary
to mix a standard deck of 52 cards is either 7 or 11 -- with the former 
number
applying when the metric used to define mixing is the total variation 
distance
and the later when it is the separation distance. This and other related
results assume all 52 cards in the deck to be distinct and require all 
$52!$
permutations of the deck to be almost equally likely for the deck to be
considered well mixed. In many instances, not all cards in the deck are
distinct and only the sets of cards dealt out to players, and not the 
order in
which they are dealt out to each player, needs to be random. We derive
transition probabilities under riffle shuffles between decks with 
repeated
cards to cover some instances of the type just described. We focus on 
decks
with cards all of which are labeled either 1 or 2 and describe the 
consequences
of having a symmetric starting deck of the form $1,...,1,2...,2$ or 
$1,2,...,
1,2$. Finally, we consider mixing times for common card games.


http://front.math.ucdavis.edu/math.PR/0503233

---------------------------------------------------------------

3336. BERMUDAN OPTION PRICING BASED ON PIECEWISE HARMONIC INTERPOLATION 
AND  THE R\'EDUITE

Frederik S. Herzberg

We consider an iterative Bermudan option pricing algorithm based on 
piecewise
harmonic interpolation and give an explicit constructive 
characterisation of
the smallest fixed point of the iteration step as the approximate price 
of the
perpetual Bermudan option. The same arguments work for a related 
iterative
algorithm based on the approximation of subharmonic functions via the 
r\'eduite
associated with a given closed $F_{\sigma}$ subset of $\RR^d$.


http://front.math.ucdavis.edu/math.PR/0503234

---------------------------------------------------------------

3337. A BRIEF NOTE ON THE SOUNDNESS OF BERMUDAN OPTION PRICING VIA 
CUBATURE

Frederik S. Herzberg

The subject of this study is an iterative Bermudan option pricing 
algorithm
based on (high-dimensional) cubature. We show that the sequence of 
Bermudan
prices (as functions of the underlying assets' logarithmic start prices)
resulting from the iteration is bounded and increases monotonely to the
approximate perpetual Bermudan option price; the convergence is linear 
in the
supremum norm with the discount factor being the convergence factor.
Furthermore, we prove a characterisation of this approximated perpetual
Bermudan price as the smallest fixed point of the iteration procedure.


http://front.math.ucdavis.edu/math.PR/0503235

---------------------------------------------------------------

3338. SPHERICAL ASYMPTOTICS FOR THE ROTOR-ROUTER MODEL IN Z^D

Lionel Levine and  Yuval Peres

The rotor-router model is a deterministic analogue of random walk 
invented by
Jim Propp. It can be used to define a deterministic aggregation model 
analogous
to internal diffusion limited aggregation. We prove an isoperimetric 
inequality
for the exit time of simple random walk from a finite region in Z^d, 
and use
this to prove that the shape of the rotor-router aggregation model in 
Z^d,
suitably rescaled, converges to a Euclidean ball in R^d.


http://front.math.ucdavis.edu/math.PR/0503251

---------------------------------------------------------------

3339. SOME EXPLICIT KREIN REPRESENTATIONS OF CERTAIN SUBORDINATORS, 
INCLUDING  THE GAMMA PROCESS

Catherine Donati-Martin (PMA) and  Marc Yor (PMA)

We give a representation of the Gamma subordinator as a Krein 
functional of
Brownian motion, using the known representations for stable 
subordinators and
Esscher transforms. In particular, we have obtained Krein 
representations of
the subordinators which govern the two parameter Poisson-Dirichlet 
family of
distributions.


http://front.math.ucdavis.edu/math.PR/0503254

---------------------------------------------------------------

3340. AN INVARIANCE PRINCIPLE FOR CONDITIONED TREES

Jean-Francois Le Gall (DMA-ENS Paris)

We consider Galton-Watson trees associated with a critical offspring
distribution and conditioned to have exactly $n$ vertices. These trees 
are
embedded in the real line by affecting spatial positions to the 
vertices, in
such a way that the increments of the spatial positions along edges of 
the tree
are independent variables distributed according to a symmetric 
probability
distribution on the real line. We then condition on the event that all 
spatial
positions are nonnegative. Under suitable assumptions on the offspring
distribution and the spatial displacements, we prove that these 
conditioned
spatial trees converge as $n\to\infty$, modulo an appropriate rescaling,
towards the conditioned Brownian tree that was studied in previous work.
Applications are given to asymptotics for random quadrangulations.


http://front.math.ucdavis.edu/math.PR/0503263

---------------------------------------------------------------

3341. ON GENERALIZED COMPUTABLE UNIVERSAL PRIORS AND THEIR CONVERGENCE

Marcus Hutter

Solomonoff unified Occam's razor and Epicurus' principle of multiple
explanations to one elegant, formal, universal theory of inductive 
inference,
which initiated the field of algorithmic information theory. His 
central result
is that the posterior of the universal semimeasure M converges rapidly 
to the
true sequence generating posterior mu, if the latter is computable. 
Hence, M is
eligible as a universal predictor in case of unknown mu. The first part 
of the
paper investigates the existence and convergence of computable universal
(semi)measures for a hierarchy of computability classes: recursive, 
estimable,
enumerable, and approximable. For instance, M is known to be 
enumerable, but
not estimable, and to dominate all enumerable semimeasures. We present 
proofs
for discrete and continuous semimeasures. The second part investigates 
more
closely the types of convergence, possibly implied by universality: in
difference and in ratio, with probability 1, in mean sum, and for 
Martin-Loef
random sequences. We introduce a generalized concept of randomness for
individual sequences and use it to exhibit difficulties regarding these 
issues.
In particular, we show that convergence fails (holds) on 
generalized-random
sequences in gappy (dense) Bernoulli classes.


http://front.math.ucdavis.edu/cs.LG/0503026

---------------------------------------------------------------

3342. THE STABLE MANIFOLD THEOREM FOR SEMILINEAR STOCHASTIC EVOLUTION  
EQUATIONS AND STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS I: THE 
STOCHASTIC
   SEMIFLOW

Salah-Eldin A Mohammed and  Tusheng Zhang and  Huaizhong Zhao

The main objective of this work is to characterize the pathwise local
structure of solutions of semilinear stochastic evolution equations 
(see's) and
stochastic partial differential equations (spde's) near stationary 
solutions.
Such characterization is realized through the long-term behavior of the
solution field near stationary points. The analysis falls in two parts 
I, II.
In Part I (this paper), we prove a general existence and compactness 
theorem
for $C^k$-cocycles of semilinear see's and spde's. Our results cover a 
large
class of semilinear see's as well as certain semilinear spde's with
non-Lipschitz terms such as stochastic reaction diffusion equations and 
the
stochastic Burgers equation with additive infinite-dimensional noise. 
In Part
II of this work ([M-Z-Z]), we establish a local stable manifold theorem 
for
non-linear see's and spde's.


http://front.math.ucdavis.edu/math.PR/0503320

---------------------------------------------------------------

3343. THE STABLE MANIFOLD THEOREM FOR SEMILINEAR STOCHASTIC EVOLUTION  
EQUATIONS AND STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS II: EXISTENCE 
OF
   STABLE AND UNSTABLE MANIFOLDS

Salah-Eldin A. Mohammed and  Tusheng Zhang and  Huaizhong Zhao

This article is a sequel to [M.Z.Z.1] aimed at completing the
characterization of the pathwise local structure of solutions of 
semilinear
stochastic evolution equations (see's) and stochastic partial 
differential
equations (spde's) near stationary solutions. Stationary solution are 
viewed as
random points in the infinite-dimensional state space, and the 
characterization
is expressed in terms of the almost sure long-time behavior of 
trajectories of
the equation in relation to the stationary solution. More specifically, 
we
establish local stable manifold theorems for semilinear see's and spde's
(Theorems 4.1-4.4). These results give smooth stable and unstable 
manifolds in
the neighborhood of a hyperbolic stationary solution of the underlying
stochastic equation. The stable and unstable manifolds are stationary, 
live in
a stationary tubular neighborhood of the stationary solution and are
asymptotically invariant under the stochastic semiflow of the see/spde. 
The
proof uses infinite-dimensional multiplicative ergodic theory 
techniques and
interpolation arguments (Theorem 2.1).


http://front.math.ucdavis.edu/math.PR/0503321

---------------------------------------------------------------

3344. BOUNDARY HARNACK PRINCIPLE FOR FRACTIONAL POWERS OF LAPLACIAN ON 
THE  SIERPINSKI CARPET

Andrzej Stos (LMP-Clermont)

We prove the Boundary Harnack Principle related to fractional powers of
Laplacian for some natural regions in the two-dimensional Sierpinski 
carpet.
This is a natual application of a probabilistic method based on the
Ikeda-Watanabe formula


http://front.math.ucdavis.edu/math.PR/0503333

---------------------------------------------------------------

3345. A NOTE ON EXACT LIKELIHOODS OF THE CARR-WU MODELS FOR LEVERAGE 
EFFECTS  AND VOLATILITY IN FINANCIAL ECONOMICS

Lancelot F. James

Recently Carr and Wu (2004, 2005) and also Huang and Wu (2004) show 
that most
stochastic processes used in traditional option pricing models can be 
cast as
special cases of time-changed L\'evy processes. In particular these are 
models
which can be tailored to exhibit correlated jumps in both the log price 
of
assets and the instantaneous volatility. Naturally similar to a recent 
work of
Barndorff-Nielsen and Shephard (2001a, b), such models may be used in a
likelihood based framework. These likelihoods are based on the 
unobserved
integrated volatility, rather than the instantaneous volatility. James 
(2005)
establishes general results for the likelihood and estimation of a 
large class
of such models which include possible leverage effects. In this note we 
show
that exact expressions for likelihood models based on generalizations 
of Carr
and Wu (2005) and Huang and Wu (2005), follow essentially from the 
arguments in
Theorem 5.1 in James (2005) with some slight modification. This serves 
to
formally verify a claim made by James (2005).


http://front.math.ucdavis.edu/math.ST/0503314

---------------------------------------------------------------

3346. POISSON KERNELS OF HALF-SPACES IN REAL HYPERBOLIC SPACES

T. Byczkowski and  P. Graczyk and  A. Stos

We provide an integral formula for the Poisson kernel of half-spaces for
Brownian motion in real hyperbolic space $\H^n$. This enables us to find
asymptotic properties of the kernel. Our starting point is the formula 
for its
Fourier transform. When $n=3$, 4 or 6 we give an explicit formula for 
the
Poisson kernel itself. In the general case we give various asymptotics 
and show
convergence to the Poisson kernel of $\H^n$.


http://front.math.ucdavis.edu/math.PR/0503372

---------------------------------------------------------------

3347. DOOB'S MAXIMAL IDENTITY, MULTIPLICATIVE DECOMPOSITIONS AND 
ENLARGEMENTS  OF FILTRATIONS

A. Nikeghbali and  M. Yor

In the theory of progressive enlargements of filtrations, the 
supermartingale
$Z_{t}=\mathbf{P}(g>t\mid \mathcal{F}_{t}) $ associated with an honest 
time
$g$, and its additive (Doob-Meyer) decomposition, play an essential 
role. In
this paper, we propose an alternative approach, using a multiplicative
representation for the supermartingale $Z_{t}$, based on Doob's maximal
identity. We thus give new examples of progressive enlargements. 
Moreover, we
give, in our setting, a proof of the decomposition formula for 
martingales,
using initial enlargement techniques, and use it to obtain some path
decompositions given the maximum or minimum of some processes.


http://front.math.ucdavis.edu/math.PR/0503386

---------------------------------------------------------------

3348. AN ANNIHILATING-BRANCHING PARTICLE MODEL FOR THE HEAT EQUATION 
WITH  AVERAGE TEMPERATURE ZERO

Krzysztof Burdzy and Jeremy Quastel

We consider two species of particles performing random walks in a 
domain in
Euclidean space with reflecting boundary conditions, which annihilate on
contact. In addition there is a conservation law so that the total 
number of
particles of each type is preserved: When the two particles of different
species annihilate each other, particles of each species, chosen at 
random,
give birth. We assume initially equal numbers of each species and show 
that the
system has a diffusive scaling limit in which the densities of the two 
species
are well approximated by the positive and negative parts of the 
solution of the
heat equation normalized to have constant $L^1$ norm. In particular, 
the higher
Neumann eigenfunctions appear as asymptotically stable states at the 
diffusive
time scale.


http://front.math.ucdavis.edu/math.PR/0503395

---------------------------------------------------------------

3349. THE REVERSIBLE NEAREST PARTICLE SYSTGEMS ON A FINITE INTERVAL

Dayue Chen and  Juxin Liu and  Fuxi Zhang

In this paper we study a one-parameter family of attractive reversible
nearest particle system on a finite interval. As the length of the 
interval
increases, the time that the nearest particle system first hits the 
empty set
increases in different order, from logarithmic to exponential, 
according to the
intensity of interaction. In particular, at the critical case, the first
hitting time increases in a polynomial order.


http://front.math.ucdavis.edu/math.PR/0503409

---------------------------------------------------------------

3350. INSIDE SINGULARITY SETS OF RANDOM GIBBS MEASURES

Julien Barral and  Stephane Seuret

We evaluate the scale at which the multifractal structure of some random
Gibbs measures becomes discernible. The value of this scale is obtained 
through
what we call the growth speed in H\"older singularity sets of a Borel 
measure.
This growth speed yields new information on the multifractal behavior 
of the
rescaled copies involved in the structure of statistically self-similar 
Gibbs
measures. Our results are useful to understand the multifractal nature 
of
various heterogeneous jump processes.


http://front.math.ucdavis.edu/math.PR/0503420

---------------------------------------------------------------

3351. RENEWAL OF SINGULARITY SETS OF STATISTICALLY SELF-SIMILAR MEASURES

Julien Barral and  Stephane Seuret

This paper investigates new properties concerning the multifractal 
structure
of a class of statistically self-similar measures. These measures 
include the
well-known Mandelbrot multiplicative cascades, sometimes called 
independent
random cascades. We evaluate the scale at which the multifractal 
structure of
these measures becomes discernible. The value of this scale is obtained 
through
what we call the growth speed in H\"older singularity sets of a Borel 
measure.
This growth speed yields new information on the multifractal behavior 
of the
rescaled copies involved in the structure of statistically self-similar
measures. Our results are useful to understand the multifractal nature 
of
various heterogeneous jump processes.


http://front.math.ucdavis.edu/math.PR/0503421

---------------------------------------------------------------

3352. A POLYHEDRAL MARKOV FIELD - PUSHING THE ARAK-SURGAILIS 
CONSTRUCTION INTO  THREE DIMENSIONS

Tomasz Schreiber

The purpose of the paper is to construct a polyhedral Markov field in
${\mathbb R}^3$ in analogy with the planar construction of the original 
Arak
(1982) polygonal Markov field. We provide a dynamic construction of the 
process
in terms of evolution of two-dimensional multi-edge systems tracing 
polyhedral
boundaries of the field in three-dimensional time-space. We also give a 
general
algorithm for simulating Gibbsian modifications of the constructed 
polyhedral
field.


http://front.math.ucdavis.edu/math.PR/0503429

---------------------------------------------------------------

3353. BAYSIAN INFERENCE VIA CLASSES OF NORMALIZED RANDOM MEASURES

Lancelot F. James and  Antonio Lijoi and Igor Pruenster

One of the main research areas in Bayesian Nonparametrics is the 
proposal and
study of priors which generalize the Dirichlet process. Here we exploit
theoretical properties of Poisson random measures in order to provide a
comprehensive Bayesian analysis of random probabilities which are 
obtained by
an appropriate normalization. Specifically we achieve explicit and 
tractable
forms of the posterior and the marginal distributions, including an 
explicit
and easily used description of generalizations of the important
Blackwell-MacQueen P\'olya urn distribution. Such simplifications are 
achieved
by the use of a latent variable which admits quite interesting 
interpretations
which allow to gain a better understanding of the behaviour of these 
random
probability measures. It is noteworthy that these models are 
generalizations of
models considered by Kingman (1975) in a non-Bayesian context. Such 
models are
known to play a significant role in a variety of applications including
genetics, physics, and work involving random mappings and assemblies. 
Hence our
analysis is of utility in those contexts as well. We also show how our 
results
may be applied to Bayesian mixture models and describe computational 
schemes
which are generalizations of known efficient methods for the case of the
Dirichlet process. We illustrate new examples of processes which can 
play the
role of priors for Bayesian nonparametric inference and finally point 
out some
interesting connections with the theory of generalized gamma 
convolutions
initiated by Thorin and further developed by Bondesson.


http://front.math.ucdavis.edu/math.ST/0503394

---------------------------------------------------------------

3354. A STOCHASTIC APPROXIMATION ALGORITHM WITH MULTIPLICATIVE STEP 
SIZE  ADAPTATION

Alexander Plakhov and  Pedro Cruz

An algorithm of searching a zero of an unknown undimensional function is
considered, measured at a point x with some error. The step sizes are 
random
positive values and are calculated according to the rule: if two 
consecutive
iterations are in same direction step is multiplied by u>1, otherwise, 
it is
multiplied by 0<d<1. The function may have one or more zeros; the 
random values
are independent and identically distributed, with zero mean and finite
variance. Under some additional assumptions on the conditions on the two
parameters u and d almost sure convergence of the sequence as well as 
under
some conditions is guaranteed almost sure divergence. In particular, if 
the
error distribuition as median 0 and zero probability for particular 
poinst then
it is established that for ud<1, convergence takes place, and for ud>1,
divergence. Due to the multiplicative rule of updating of the step, it 
is
natural to expect that the sequence converges rapidly: like a geometric
progression (if convergence takes place), but the limit value may not 
coincide
with, but instead, approximates one of zeros of the function. By 
adjusting the
parameters u and d, one can reach necessary precision of approximation; 
higher
precision is obtained at the expense of lower convergence rate.


http://front.math.ucdavis.edu/math.ST/0503434

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3355. ON APPROXIMATE PATTERN MATCHING FOR A CLASS OF GIBBS RANDOM FIELDS

J.R. Chazottes and  F. Redig and  E. Verbitskiy

We prove an exponential approximation for the law of approximate 
occurrence
of typical patterns for a class of Gibbsian sources on the lattice 
$\mathbb
Z^d$, $d\ge 2$. From this result, we deduce a law of large numbers and 
a large
deviation result for the the waiting time of distorted patterns.


http://front.math.ucdavis.edu/math.PR/0503008

---------------------------------------------------------------

3356. THE BASIC REPRESENTATION OF THE CURRENT GROUP O(N,1)^X IN THE L^2 
SPACE  OVER THE GENERALIZED LEBESGUE MEASURE

A.M.Vershik and  M.I.Graev

We give the realization of the representation of the current group 
O(n,1)^X
where X is a manifold, in the Hilbert space of L^2(F,\nu) of 
functionals on the
the space F of the generalized functions on the manifold X which are 
square
integrable over measure \nu which is related to a distinguish Levy 
process with
values in R^{n-1} which generalized one dimensional gamma process. 
Unipotent
subgroup of the group O(n,1)^X acts as the group of multiplicators. 
Measure \nu
is sigma-finite and invariant under the action current group O(n-1)^X. 
Ther
case of n=2 (SL(2,R^X)) was considered before in the series of papers 
starting
from the article Vershik-Gel'fand-Graev (1973).


http://front.math.ucdavis.edu/math.RT/0503404

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3357. DYNAMIC IMPORTANCE SAMPLING FOR UNIFORMLY RECURRENT MARKOV CHAINS

Paul Dupuis and Hui Wang

Importance sampling is a variance reduction technique for efficient
estimation of rare-event probabilities by Monte Carlo. In standard 
importance
sampling schemes, the system is simulated using an a priori fixed 
change of
measure suggested by a large deviation lower bound analysis. Recent 
work,
however, has suggested that such schemes do not work well in many 
situations.
In this paper we consider dynamic importance sampling in the setting of
uniformly recurrent Markov chains. By ``dynamic'' we mean that in the 
course of
a single simulation, the change of measure can depend on the outcome of 
the
simulation up till that time. Based on a control-theoretic approach to 
large
deviations, the existence of asymptotically optimal dynamic schemes is
demonstrated in great generality. The implementation of the dynamic 
schemes is
carried out with the help of a limiting Bellman equation. Numerical 
examples
are presented to contrast the dynamic and standard schemes.


http://front.math.ucdavis.edu/math.PR/0503454

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3358. THE EXIT PROBLEM FOR DIFFUSIONS WITH TIME-PERIODIC DRIFT AND 
STOCHASTIC  RESONANCE

Samuel Herrmann and Peter Imkeller

Physical notions of stochastic resonance for potential diffusions in
periodically changing double-well potentials such as the spectral power
amplification have proved to be defective. They are not robust for the 
passage
to their effective dynamics: continuous-time finite-state Markov chains
describing the rough features of transitions between different domains 
of
attraction of metastable points. In the framework of one-dimensional 
diffusions
moving in periodically changing double-well potentials we design a new 
notion
of stochastic resonance which refines Freidlin's concept of 
quasi-periodic
motion. It is based on exact exponential rates for the transition 
probabilities
between the domains of attraction which are robust with respect to the 
reduced
Markov chains. The quality of periodic tuning is measured by the 
probability
for transition during fixed time windows depending on a time scale 
parameter.
Maximizing it in this parameter produces the stochastic resonance 
points.


http://front.math.ucdavis.edu/math.PR/0503455

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3359. LEARNING MIXTURES OF SEPARATED NONSPHERICAL GAUSSIANS

Sanjeev Arora and Ravi Kannan

Mixtures of Gaussian (or normal) distributions arise in a variety of
application areas. Many heuristics have been proposed for the task of 
finding
the component Gaussians given samples from the mixture, such as the EM
algorithm, a local-search heuristic from Dempster, Laird and Rubin [J. 
Roy.
Statist. Soc. Ser. B 39 (1977) 1-38]. These do not provably run in 
polynomial
time. We present the first algorithm that provably learns the component
Gaussians in time that is polynomial in the dimension. The Gaussians 
may have
arbitrary shape, but they must satisfy a ``separation condition'' which 
places
a lower bound on the distance between the centers of any two component
Gaussians. The mathematical results at the heart of our proof are 
``distance
concentration'' results--proved using isoperimetric inequalities--which
establish bounds on the probability distribution of the distance 
between a pair
of points generated according to the mixture. We also formalize the more
general problem of max-likelihood fit of a Gaussian mixture to 
unstructured
data.


http://front.math.ucdavis.edu/math.PR/0503457

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3360. FAST SIMULATION OF NEW COINS FROM OLD

Serban Nacu and Yuval Peres

Let S\subset (0,1). Given a known function f:S\to (0,1), we consider the
problem of using independent tosses of a coin with probability of heads 
p
(where p\in S is unknown) to simulate a coin with probability of heads 
f(p). We
prove that if S is a closed interval and f is real analytic on S, then 
f has a
fast simulation on S (the number of p-coin tosses needed has exponential
tails). Conversely, if a function f has a fast simulation on an open 
set, then
it is real analytic on that set.


http://front.math.ucdavis.edu/math.PR/0503458

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3361. STRUCTURE OF LARGE RANDOM HYPERGRAPHS

R. W. R. Darling and J. R. Norris

The theme of this paper is the derivation of analytic formulae for 
certain
large combinatorial structures. The formulae are obtained via fluid 
limits of
pure jump-type Markov processes, established under simple conditions on 
the
Laplace transforms of their Levy kernels. Furthermore, a related 
Gaussian
approximation allows us to describe the randomness which may persist in 
the
limit when certain parameters take critical values. Our method is quite
general, but is applied here to vertex identifiability in random 
hypergraphs. A
vertex v is identifiable in n steps if there is a hyperedge containing 
v all of
whose other vertices are identifiable in fewer steps.
   We say that a hyperedge is identifiable if every one of its vertices 
is
identifiable. Our analytic formulae describe the asymptotics of the 
number of
identifiable vertices and the number of identifiable hyperedges for a
Poisson(\beta) random hypergraph \Lambda on a set V of N vertices, in 
the limit
as N\to \infty. Here \beta is a formal power series with nonnegative
coefficients \beta_0,\beta_1,..., and (\Lambda(A))_{A\subseteq V} are
independent Poisson random variables such that \Lambda(A), the number of
hyperedges on A, has mean N\beta_j/\pmatrixN j whenever |A|=j.


http://front.math.ucdavis.edu/math.PR/0503460

---------------------------------------------------------------

3362. LARGE DEVIATIONS FOR TEMPLATE MATCHING BETWEEN POINT PROCESSES

Zhiyi Chi

We study the asymptotics related to the following matching criteria for 
two
independent realizations of point processes X\sim X and Y\sim Y. Given 
l>0,
X\cap [0,l) serves as a template. For each t>0, the matching score 
between the
template and Y\cap [t,t+l) is a weighted sum of the Euclidean distances 
from
y-t to the template over all y\in Y\cap [t,t+l). The template matching 
criteria
are used in neuroscience to detect neural activity with certain 
patterns. We
first consider W_l(\theta), the waiting time until the matching score 
is above
a given threshold \theta. We show that whether the score is scalar- or
vector-valued, (1/l)\log W_l(\theta) converges almost surely to a 
constant
whose explicit form is available, when X is a stationary ergodic 
process and Y
is a homogeneous Poisson point process. Second, as l\to\infty, a strong
approximation for -\log [\Pr{W_l(\theta)=0}] by its rate function is
established, and in the case where X is sufficiently mixing, the rates, 
after
being centered and normalized by \sqrtl, satisfy a central limit 
theorem and
almost sure invariance principle. The explicit form of the variance of 
the
normal distribution is given for the case where X is a homogeneous 
Poisson
process as well.


http://front.math.ucdavis.edu/math.PR/0503463

---------------------------------------------------------------

3363. RANDOM K-SAT: TWO MOMENTS SUFFICE TO CROSS A SHARP THRESHOLD

Dimitris Achlioptas and Cristopher Moore

Many NP-complete constraint satisfaction problems appear to undergo a 
"phase
transition'' from solubility to insolubility when the constraint 
density passes
through a critical threshold. In all such cases it is easy to derive 
upper
bounds on the location of the threshold by showing that above a certain 
density
the first moment (expectation) of the number of solutions tends to 
zero. We
show that in the case of certain symmetric constraints, considering the 
second
moment of the number of solutions yields nearly matching lower bounds 
for the
location of the threshold. Specifically, we prove that the threshold 
for both
random hypergraph 2-colorability (Property B) and random Not-All-Equal 
k-SAT is
2^{k-1} ln 2 -O(1). As a corollary, we establish that the threshold for 
random
k-SAT is of order Theta(2^k), resolving a long-standing open problem.


http://front.math.ucdavis.edu/cond-mat/0310227

---------------------------------------------------------------

3364. DISTRIBUTION OF THE SIZE OF A LARGEST PLANAR MATCHING AND LARGEST 
PLANAR  SUBGRAPH IN RANDOM BIPARTITE GRAPHS

Marcos Kiwi and  Martin Loebl

We address the following question: When a randomly chosen regular 
bipartite
multi--graph is drawn in the plane in the ``standard way'', what is the
distribution of its maximum size planar matching (set of non--crossing 
disjoint
edges) and maximum size planar subgraph (set of non--crossing edges 
which may
share endpoints)? The problem is a generalization of the Longest 
Increasing
Sequence (LIS) problem (also called Ulam's problem). We present 
combinatorial
identities which relate the number of $r$-regular bipartite 
multi--graphs with
maximum planar matching (maximum planar subgraph)of at most $d$ edges 
to a
signed sum of restricted lattice walks in $\ZZ^d$, and to the number of 
pairs
of standard Young tableaux of the same shape and with a 
``descend--type''
property. Our results are obtained via generalizations of two 
combinatorial
proofs through which Gessel's identity can be obtained (an identity 
that is
crucial in the derivation of a bivariate generating function associated 
to the
distribution of LISs, and key to the analytic attack on Ulam's problem).


http://front.math.ucdavis.edu/math.CO/0503465

---------------------------------------------------------------

3365. THE SHANNON INFORMATION OF FILTRATIONS AND THE ADDITIONAL 
LOGARITHMIC  UTILITY OF INSIDERS

Stefan Ankirchner and  Steffen Dereich and Peter Imkeller

The background for the general mathematical link between utility and
information theory investigated in this paper is a simple financial 
market
model with two kinds of small traders: less informed traders and 
insiders,
whose extra information is represented by an enlargement of the other 
agents'
filtration. The expected logarithmic utility increment, i.e. the 
difference of
the insider's and the less informed trader's expected logarithmic 
utility is
described in terms of the information drift, i.e. the drift one has to
eliminate in order to perceive the price dynamics as a martingale from 
the
insider's perspective. On the one hand, we describe the information 
drift in a
very general setting by natural quantities expressing the probabilistic 
better
informed view of the world. This on the other hand allows us to 
identify the
additional utility by entropy related quantities known from information 
theory.
In particular, in a complete market in which the insider has some fixed
additional information during the entire trading interval, its utility
increment can be represented by the Shannon information of his extra 
knowledge.
For general markets, and in some particular examples, we provide 
estimates of
maximal utility by information inequalities.


http://front.math.ucdavis.edu/math.PR/0503013

---------------------------------------------------------------

3366. DIFFUSION MAPS, SPECTRAL CLUSTERING AND REACTION COORDINATES OF  
DYNAMICAL SYSTEMS

Boaz Nadler and  Stephane Lafon and  Ronald R. Coifman and  Ioannis G. 
Kevrekidis

A central problem in data analysis is the low dimensional 
representation of
high dimensional data, and the concise description of its underlying 
geometry
and density. In the analysis of large scale simulations of complex 
dynamical
systems, where the notion of time evolution comes into play, important 
problems
are the identification of slow variables and dynamically meaningful 
reaction
coordinates that capture the long time evolution of the system. In this 
paper
we provide a unifying view of these apparently different tasks, by 
considering
a family of {\em diffusion maps}, defined as the embedding of complex 
(high
dimensional) data onto a low dimensional Euclidian space, via the 
eigenvectors
of suitably defined random walks defined on the given datasets. 
Assuming that
the data is randomly sampled from an underlying general probability
distribution $p(\x)=e^{-U(\x)}$, we show that as the number of samples 
goes to
infinity, the eigenvectors of each diffusion map converge to the 
eigenfunctions
of a corresponding differential operator defined on the support of the
probability distribution. Different normalizations of the Markov chain 
on the
graph lead to different limiting differential operators. One 
normalization
gives the Fokker-Planck operators with the same potential U(x), best 
suited for
the study of stochastic differential equations as well as for 
clustering.
Another normalization gives the Laplace-Beltrami (heat) operator on the
manifold in which the data resides, best suited for the analysis of the
geometry of the dataset, regardless of its possibly non-uniform density.


http://front.math.ucdavis.edu/math.NA/0503445

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3367. TRADING STRATEGY ADIPTED OPTIMIZATION OF EUROPEAN CALL OPTION

Toshio Fukumi

Optimal pricing of European call option is described by linear 
stochastic
differential equation. Trading strategy given by a twin of stochastic 
variables
was integrated w.r.t. Black-Scholes formula to adopt optimal pricing to
tarading strategy.


http://front.math.ucdavis.edu/math.OC/0503444

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3368. CHARACTERIZATION OF ARBITRAGE-FREE MARKETS

Eva Strasser

The present paper deals with the characterization of no-arbitrage 
properties
of a continuous semimartingale. The first main result, Theorem
\refMainTheoremCharNA, extends the no-arbitrage criterion by Levental 
and
Skorohod [Ann. Appl.
   Probab. 5 (1995) 906-925] from diffusion processes to arbitrary 
continuous
semimartingales. The second main result, Theorem 2.4, is a 
characterization of
a weaker notion of no-arbitrage in terms of the existence of 
supermartingale
densities. The pertaining weaker notion of no-arbitrage is equivalent 
to the
absence of immediate arbitrage opportunities, a concept introduced by 
Delbaen
and Schachermayer [Ann. Appl. Probab. 5 (1995) 926-945]. Both results 
are
stated in terms of conditions for any semimartingales starting at 
arbitrary
stopping times \sigma. The necessity parts of both results are known 
for the
stopping time \sigma=0 from Delbaen and Schachermayer [Ann. Appl. 
Probab. 5
(1995) 926-945]. The contribution of the present paper is the proofs of 
the
corresponding sufficiency parts.


http://front.math.ucdavis.edu/math.PR/0503473

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3369. GAUSSIAN LIMITS FOR RANDOM MEASURES IN GEOMETRIC PROBABILITY

Yu. Baryshnikov and J. E. Yukich

We establish Gaussian limits for general measures induced by binomial 
and
Poisson point processes in d-dimensional space. The limiting Gaussian 
field has
a covariance functional which depends on the density of the point 
process. The
general results are used to deduce central limit theorems for measures 
induced
by random graphs (nearest neighbor, Voronoi and sphere of influence 
graph),
random sequential packing models (ballistic deposition and spatial 
birth-growth
models) and statistics of germ-grain models.


http://front.math.ucdavis.edu/math.PR/0503474

---------------------------------------------------------------

3370. ON THE DISTRIBUTION OF THE MAXIMUM OF A GAUSSIAN FIELD WITH D 
PARAMETERS

Jean-Marc Azais and Mario Wschebor

Let I be a compact d-dimensional manifold, let X:I\to R be a Gaussian 
process
with regular paths and let F_I(u), u\in R, be the probability 
distribution
function of sup_{t\in I}X(t). We prove that under certain regularity and
nondegeneracy conditions, F_I is a C^1-function and satisfies a certain
implicit equation that permits to give bounds for its values and to 
compute its
asymptotic behavior as u\to +\infty. This is a partial extension of 
previous
results by the authors in the case d=1. Our methods use strongly the 
so-called
Rice formulae for the moments of the number of roots of an equation of 
the form
Z(t)=x, where Z:I\to R^d is a random field and x is a fixed point in 
R^d. We
also give proofs for this kind of formulae, which have their own 
interest
beyond the present application.


http://front.math.ucdavis.edu/math.PR/0503475

---------------------------------------------------------------

3371. HEAVY TRAFFIC ANALYSIS OF OPEN PROCESSING NETWORKS WITH COMPLETE  
RESOURCE POOLING: ASYMPTOTIC OPTIMALITY OF DISCRETE REVIEW POLICIES

Baris Ata and Sunil Kumar

We consider a class of open stochastic processing networks, with 
feedback
routing and overlapping server capabilities, in heavy traffic. The 
networks we
consider satisfy the so-called complete resource pooling condition and
therefore have one-dimensional approximating Brownian control problems.
   We propose a simple discrete review policy for controlling such 
networks.
   Assuming 2+\epsilon moments on the interarrival times and processing 
times,
we provide a conceptually simple proof of asymptotic optimality of the 
proposed
policy.


http://front.math.ucdavis.edu/math.PR/0503477

---------------------------------------------------------------

3372. A CHARACTERIZATION OF THE OPTIMAL RISK-SENSITIVE AVERAGE COST IN 
FINITE  CONTROLLED MARKOV CHAINS

Rolando Cavazos-Cadena and Daniel Hernandez-Hernandez

This work concerns controlled Markov chains with finite state and action
spaces. The transition law satisfies the simultaneous Doeblin 
condition, and
the performance of a control policy is measured by the (long-run)
risk-sensitive average cost criterion associated to a positive, but 
otherwise
arbitrary, risk sensitivity coefficient. Within this context, the 
optimal
risk-sensitive average cost is characterized via a minimization problem 
in a
finite-dimensional Euclidean space.


http://front.math.ucdavis.edu/math.PR/0503478

---------------------------------------------------------------

3373. LARGE DEVIATIONS OF THE EMPIRICAL VOLUME FRACTION FOR STATIONARY 
POISSON  GRAIN MODELS

Lothar Heinrich

We study the existence of the (thermodynamic) limit of the scaled
cumulant-generating function L_n(z)=|W_n|^{-1}\logE\exp{z|\Xi\cap W_n|} 
of the
empirical volume fraction |\Xi\cap W_n|/|W_n|, where |\cdot| denotes the
d-dimensional Lebesgue measure. Here \Xi=\bigcup_{i\ge1}(\Xi_i+X_i) 
denotes a
d-dimensional Poisson grain model (also known as a Boolean model) 
defined by a
stationary Poisson process \Pi_{\lambda}=\sum_{i\ge1}\delta_{X_i} with
intensity \lambda >0 and a sequence of independent copies 
\Xi_1,\Xi_2,... of a
random compact set \Xi_0. For an increasing family of compact convex 
sets {W_n,
n\ge1} which expand unboundedly in all directions, we prove the 
existence and
analyticity of the limit lim_{n\to\infty}L_n(z) on some disk in the 
complex
plane whenever E\exp{a|\Xi_0|}<\infty for some a>0. Moreover, closely 
connected
with this result, we obtain exponential inequalities and the exact 
asymptotics
for the large deviation probabilities of the empirical volume fraction 
in the
sense of Cram\'er and Chernoff.


http://front.math.ucdavis.edu/math.PR/0503479

From pas at www.economia.unimi.it  Mon May  2 17:11:43 2005
From: pas at www.economia.unimi.it (pas@www.economia.unimi.it)
Date: Mon May  2 17:38:13 2005
Subject: [Pas] Probability Abstract 86
Message-ID: <02e4d6c8a2eaec0fe169cee3b85e8578@unimi.it>

                                                                         
                         May 2, 2005
                                                                         
                         Letter 86

Probability Abstract Service



---------------------------------------------------------------

3205. RANDOM GRAPHS WITH ARBITRARY I.I.D. DEGREES

Remco van der Hofstad and  Gerard Hooghiemstra and  Dmitri Znamenski

In this paper we study distances and connectivity properties of random 
graphs
with an arbitrary i.i.d. degree sequence. When the tail of the degree
distribution is regularly varying with exponent $1-\tau$ there are three
distinct cases: (i) $\tau>3$, where the degrees have finite variance, 
(ii)
$\tau\in (2,3)$, where the degrees have infinite variance, but finite 
mean, and
(iii) $\tau\in (1,2)$, where the degrees have infinite mean. These 
random
graphs can serve as models for complex networks where degree power laws 
are
observed. The distances between pairs of nodes in the three cases 
mentioned
above have been studied in three previous publications, and we survey 
the
results obtained there. Apart from the critical cases $\tau=1$, 
$\tau=2$ and
$\tau=3$, this completes the scaling picture. We explain the results
heuristically and describe related work and open problems. We also 
compare the
behavior in this model to Internet data, where a degree power law with 
exponent
$\tau\approx 2.2$ is observed.
   Furthermore, in this paper we derive results concerning the connected
components and the diameter. We give a criterion when there exists a 
unique
largest connected component of size proportional to the size of the 
graph, and
study sizes of the other connected components. Also, we show that for 
$\tau\in
(2,3)$, which is most often observed in real networks, the diameter in 
this
model grows much faster than the typical distance between two arbitrary 
nodes.


http://front.math.ucdavis.edu/math.PR/0502580

---------------------------------------------------------------

3206. THE SINGLE SERVER QUEUE AND THE STORAGE MODEL: LARGE DEVIATIONS 
AND  FIXED POINTS

Moez Draief

We consider the coupling of a single server queue and a storage model 
defined
as a Queue/Store model in Draief et al. 2004. We establish that if the 
input
variables both arrivals to the queue and to the store satisfy large 
deviations
principles and are linked through an {\em exponential tilting} than the 
output
variables (departures from each system) satisfy large deviations 
principles
with the same rate function. This generalizes to the context of large
deviations the extension of Burke's Theorem derived in Draief et al. 
2004.


http://front.math.ucdavis.edu/math.PR/0503016

---------------------------------------------------------------

3207. SUBEXPONENTIAL ASYMPTOTICS OF HYBRID FLUID AND RUIN MODELS

Bert Zwart and  Sem Borst and Krzystof Debicki

We investigate the tail asymptotics of the supremum of X(t)+Y(t)-ct, 
where
X={X(t),t\geq 0} and Y={Y(t),t\geq 0} are two independent stochastic 
processes.
We assume that the process Y has subexponential characteristics and 
that the
process X is more regular in a certain sense than Y. A key issue 
examined in
earlier studies is under what conditions the process X contributes to 
large
values of the supremum only through its average behavior. The present 
paper
studies various scenarios where the latter is not the case, and the 
process X
shows some form of ``atypical'' behavior as well. In particular, we 
consider a
fluid model fed by a Gaussian process X and an (integrated) On-Off 
process Y.
We show that, depending on the model parameters, the Gaussian process 
may
contribute to the tail asymptotics by its moderate deviations, large
deviations, or oscillatory behavior.


http://front.math.ucdavis.edu/math.PR/0503482

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3208. DEVIATION INEQUALITIES VIA COUPLING FOR STOCHASTIC PROCESSES AND 
RANDOM  FIELDS

J.-R. Chazottes and  P. Collet and  C. Kuelske and  F. Redig

We present a new and simple approach to deviation inequalities for
non-product measures, i.e., for dependent random variables. Our method 
is based
on coupling. We illustrate our abstract results with chains with 
complete
connections and Gibbsian random fields, both at high and low 
temperature.


http://front.math.ucdavis.edu/math.PR/0503483

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3209. AN APPROXIMATE SAMPLING FORMULA UNDER GENETIC HITCHHIKING

A. M. Etheridge and  P. Pfaffelhuber and A. Wakolbinger

For a genetic locus carrying a strongly beneficial allele which has just
fixed in a large population we study the ancestry at a linked neutral 
locus.
During this ''selective sweep'' the linkage between the two loci is 
broken up
by recombination, and the ancestry at the neutral locus is modelled by a
structured coalescent in a random background. For large selection 
coefficients
$\alpha$ and under an appropriate scaling of the recombination rate, we 
derive
a sampling formula with an order of accuracy of $O((\log\alpha)^{-2})$ 
in
probability. In particular we see that, with this order of accuracy, in 
a
sample of fixed size there are at most two non-singleton families of
individuals which are identi cal by descent at the neutral locus from 
the
beginning of the sweep. This refines a formula going back to the work of
Maynard Smith and Haigh, and co mplements recent work of Schweinsberg 
and
Durrett on selective sweeps in the Moran model.


http://front.math.ucdavis.edu/math.PR/0503485

---------------------------------------------------------------

3210. LARGE DEVIATIONS OF A MODIFIED JACKSON NETWORK: STABILITY AND 
ROUGH  ASYMPTOTICS

Robert D. Foley and David R. McDonald

Consider a modified, stable, two node Jackson network where server 2 
helps
server 1 when server 2 is idle. The probability of a large deviation of 
the
number of customers at node one can be calculated using the flat 
boundary
theory of Schwartz and Weiss [Large Deviations Performance Analysis 
(1994),
  Chapman and Hall, New York]. Surprisingly, however, these calculations 
show
that the proportion of time spent on the boundary, where server 2 is 
idle, may
be zero. This is in sharp contrast to the unmodified Jackson network 
which
spends a nonzero proportion of time on this boundary.


http://front.math.ucdavis.edu/math.PR/0503487

---------------------------------------------------------------

3211. BRIDGES AND NETWORKS: EXACT ASYMPTOTICS

Robert D. Foley and David R. McDonald

We extend the Markov additive methodology developed in [Ann. Appl. 
Probab. 9
(1999) 110-145, Ann. Appl. Probab. 11 (2001) 596-607] to obtain the 
sharp
asymptotics of the steady state probability of a queueing network when 
one of
the nodes gets large. We focus on a new phenomenon we call a bridge. 
The bridge
cases occur when the Markovian part of the twisted Markov additive 
process is
one null recurrent or one transient, while the jitter cases treated in 
[Ann.
Appl. Probab. 9 (1999) 110-145, Ann. Appl. Probab. 11 (2001) 596-607] 
occur
when the Markovian part is (one) positive recurrent. The asymptotics of 
the
steady state is an exponential times a polynomial term in the bridge 
case, but
is purely exponential in the jitter case. We apply this theory to a 
modified,
stable, two node Jackson network where server two helps server one when 
server
two is idle. We derive the sharp asymptotics of the steady state 
distribution
of the number of customers queued at each node as the number of 
customers
queued at the server one grows large. In so doing we get an intuitive
understanding of the companion paper [Ann. Appl. Probab. 15 (2005) 
519-541]
which gives a large deviation analysis of this problem using the flat 
boundary
theory in the book by Shwartz and Weiss. Unlike the (unscaled) large 
deviation
path of a Jackson network which jitters along the boundary, the 
unscaled large
deviation path of the modified network tries to avoid the boundary 
where server
two helps server one (and forms a bridge).


http://front.math.ucdavis.edu/math.PR/0503488

---------------------------------------------------------------

3212. UPPER BOUNDS FOR SPATIAL POINT PROCESS APPROXIMATIONS

Dominic Schuhmacher

We consider the behavior of spatial point processes when subjected to a 
class
of linear transformations indexed by a variable T. It was shown in 
Ellis [Adv.
in Appl. Probab. 18 (1986) 646-659] that, under mild assumptions, the
transformed processes behave approximately like Poisson processes for 
large T.
In this article, under very similar assumptions, explicit upper bounds 
are
given for the d_2-distance between the corresponding point process
distributions. A number of related results, and applications to kernel 
density
estimation and long range dependence testing are also presented. The 
main
results are proved by applying a generalized Stein-Chen method to 
discretized
versions of the point processes.


http://front.math.ucdavis.edu/math.PR/0503491

---------------------------------------------------------------

3213. NOISE STABILITY OF FUNCTIONS WITH LOW INFLUENCES: INVARIANCE AND  
OPTIMALITY

Elchanan Mossel and Ryan O'Donnell and Krzysztof Oleszkiewicz

In this paper we study functions with low influences on product 
probability
spaces. The analysis of boolean functions with low influences has 
become a
central problem in discrete Fourier analysis. It is motivated by 
fundamental
questions arising from the construction of probabilistically checkable 
proofs
in theoretical computer science and from problems in the theory of 
social
choice in economics.
   We prove an invariance principle for multilinear polynomials with low
influences and bounded degree; it shows that under mild conditions the
distribution of such polynomials is essentially invariant for all 
product
spaces. Ours is one of the very few known non-linear invariance 
principles. It
has the advantage that its proof is simple and that the error bounds are
explicit. We also show that the assumption of bounded degree can be 
eliminated
if the polynomials are slightly ``smoothed''; this extension is 
essential for
our applications to ``noise stability''-type problems.
   In particular, as applications of the invariance principle we prove 
two
conjectures: the ``Majority Is Stablest'' conjecture from theoretical 
computer
science, which was the original motivation for this work, and the ``It 
Ain't
Over Till It's Over'' conjecture from social choice theory.


http://front.math.ucdavis.edu/math.PR/0503503

---------------------------------------------------------------

3214. LOGARITHMIC SOBOLEV INEQUALITY FOR LOG-CONCAVE MEASURE FROM  
PREKOPA-LEINDLER INEQUALITY

Ivan Gentil

We develop in this paper an amelioration of the method given by S. 
Bobkov and
M. Ledoux in GAFA (2000). We prove by Prekopa-Leindler Theorem an 
optimal
modified logarithmic Sobolev inequality adapted for all log-concave 
measure on
$\dR^n$. This inequality implies results proved by Bobkov and Ledoux, 
the
Euclidean Logarithmic Sobolev inequality generalized in the last years 
and it
also implies some convex logarithmic Sobolev inequalities for large 
entropy.


http://front.math.ucdavis.edu/math.FA/0503476

---------------------------------------------------------------

3215. EQUILIBRIUM GLAUBER AND KAWASAKI DYNAMICS OF CONTINUOUS PARTICLE 
SYSTEMS

Yu. G. Kondratiev and  E. Lytvynov and  M. R\"ockner

We construct two types of equilibrium dynamics of infinite particle 
systems
in a Riemannian manifold $X$. These dynamics are analogs of the Glauber,
respectively Kawasaki dynamics of lattice spin systems. The Glauber 
dynamics
now is a process where interacting particles randomly appear and 
disappear,
i.e., it is a birth-and-death process in $X$, while in the Kawasaki 
dynamics
interacting particles randomly jump over $X$. We establish conditions 
on a
priori explicitly given symmetrizing measures and generators of both 
dynamics
under which corresponding conservative Markov processes exist.


http://front.math.ucdavis.edu/math.PR/0503042

---------------------------------------------------------------

3216. THE STEPPING STONE MODEL. II: GENEALOGIES AND THE INFINITE SITES 
MODEL

Iljana Zahle and  J. Theodore Cox and Richard Durrett

This paper extends earlier work by Cox and Durrett, who studied the
coalescence times for two lineages in the stepping stone model on the
two-dimensional torus. We show that the genealogy of a sample of size n 
is
given by a time change of Kingman's coalescent. With DNA sequence data 
in mind,
we investigate mutation patterns under the infinite sites model, which 
assumes
that each mutation occurs at a new site. Our results suggest that the 
spatial
structure of the human population contributes to the haplotype 
structure and a
slower than expected decay of genetic correlation with distance 
revealed by
recent studies of the human genome.


http://front.math.ucdavis.edu/math.PR/0503512

---------------------------------------------------------------

3217. RENEWAL THEORY AND COMPUTABLE CONVERGENCE RATES FOR GEOMETRICALLY 
  ERGODIC MARKOV CHAINS

Peter H. Baxendale

We give computable bounds on the rate of convergence of the transition
probabilities to the stationary distribution for a certain class of
geometrically ergodic Markov chains. Our results are different from 
earlier
estimates of Meyn and Tweedie, and from estimates using coupling, 
although we
start from essentially the same assumptions of a drift condition toward 
a
``small set.'' The estimates show a noticeable improvement on existing 
results
if the Markov chain is reversible with respect to its stationary 
distribution,
and especially so if the chain is also positive. The method of proof 
uses the
first-entrance-last-exit decomposition, together with new quantitative 
versions
of a result of Kendall from discrete renewal theory.


http://front.math.ucdavis.edu/math.PR/0503515

---------------------------------------------------------------

3218. UTILITY MAXIMIZATION WITH A STOCHASTIC CLOCK AND AN UNBOUNDED 
RANDOM  ENDOWMENT

Gordan Zitkovic

We introduce a linear space of finitely additive measures to treat the
problem of optimal expected utility from consumption under a stochastic 
clock
and an unbounded random endowment process. In this way we establish 
existence
and uniqueness for a large class of utility-maximization problems 
including the
classical ones of terminal wealth or consumption, as well as the 
problems that
depend on a random time horizon or multiple consumption instances. As an
example we explicitly treat the problem of maximizing the logarithmic 
utility
of a consumption stream, where the local time of an Ornstein-Uhlenbeck 
process
acts as a stochastic clock.


http://front.math.ucdavis.edu/math.PR/0503516

---------------------------------------------------------------

3219. RECONSTRUCTING A TWO-COLOR SCENERY BY OBSERVING IT ALONG A SIMPLE 
RANDOM  WALK PATH

Heinrich Matzinger

Let {\xi (n)}_{n\in Z} be a two-color random scenery, that is, a random
coloring of Z in two colors, such that the \xi (i)'s are i.i.d. 
Bernoulli
variables with parameter \tfrac12. Let {S(n)}_{n\in N} be a symmetric 
random
walk starting at 0. Our main result shows that a.s., \xi \circ S (the
composition of \xi and S) determines \xi up to translation and 
reflection. In
other words, by observing the scenery \xi along the random walk path S, 
we can
a.s. reconstruct \xi up to translation and reflection. This result 
gives a
positive answer to the question of H. Kesten of whether one can a.s. 
detect a
single defect in almost every two-color random scenery by observing it 
only
along a random walk path.


http://front.math.ucdavis.edu/math.PR/0503517

---------------------------------------------------------------

3220. A DIFFUSION MODEL OF SCHEDULING CONTROL IN QUEUEING SYSTEMS WITH 
MANY  SERVERS

Rami Atar

This paper studies a diffusion model that arises as the limit of a 
queueing
system scheduling problem in the asymptotic heavy traffic regime of 
Halfin and
Whitt. The queueing system consists of several customer classes and many
servers working in parallel, grouped in several stations. Servers in 
different
stations offer service to customers of each class at possibly different 
rates.
The control corresponds to selecting what customer class each server 
serves at
each time. The diffusion control problem does not seem to have explicit
solutions and therefore a characterization of optimal solutions via the
Hamilton-Jacobi-Bellman equation is addressed. Our main result is the 
existence
and uniqueness of solutions of the equation. Since the model is set on 
an
unbounded domain and the cost per unit time is unbounded, the analysis 
requires
estimates on the state process that are subexponential in the time 
variable. In
establishing these estimates, a key role is played by an integral 
formula that
relates queue length and idle time processes, which may be of 
independent
interest.


http://front.math.ucdavis.edu/math.PR/0503518

---------------------------------------------------------------

3221. EXACT AND APPROXIMATE RESULTS FOR DEPOSITION AND ANNIHILATION 
PROCESSES  ON GRAPHS

Mathew D. Penrose and Aidan Sudbury

We consider random sequential adsorption processes where the initially 
empty
sites of a graph are irreversibly occupied, in random order, either by 
monomers
which block neighboring sites, or by dimers. We also consider a process 
where
initially occupied sites annihilate their neighbors at random times. We 
verify
that these processes are well defined on infinite graphs, and derive 
forward
equations governing joint vacancy/occupation probabilities. Using 
these, we
derive exact formulae for occupation probabilities and pair 
correlations in
Bethe lattices. For the blocking and annihilation processes we also 
prove
positive correlations between sites an even distance apart, and for 
blocking we
derive rigorous lower bounds for the site occupation probability in 
lattices,
including a lower bound of 1/3 for Z^2. We also give normal 
approximation
results for the number of occupied sites in a large finite graph.


http://front.math.ucdavis.edu/math.PR/0503519

---------------------------------------------------------------

3222. NEAR-INTEGRATED GARCH SEQUENCES

Istvan Berkes and  Lajos Horvath and Piotr Kokoszka

Motivated by regularities observed in time series of returns on 
speculative
assets, we develop an asymptotic theory of GARCH(1,1) processes {y_k} 
defined
by the equations y_k=\sigma_k\epsilon_k, \sigma_k^2=\omega +\alpha
y_{k-1}^2+\beta \sigma_{k-1}^2 for which the sum \alpha +\beta 
approaches unity
as the number of available observations tends to infinity. We call such
sequences near-integrated. We show that the asymptotic behavior of
near-integrated GARCH(1,1) processes critically depends on the sign of 
\gamma
:=\alpha +\beta -1. We find assumptions under which the solutions 
exhibit
increasing oscillations and show that these oscillations grow 
approximately
like a power function if \gamma \leq 0 and exponentially if \gamma >0. 
We
establish an additive representation for the near-integrated GARCH(1,1)
processes which is more convenient to use than the traditional 
multiplicative
Volterra series expansion.


http://front.math.ucdavis.edu/math.PR/0503520

---------------------------------------------------------------

3223. ASYMPTOTICS IN RANDOMIZED URN MODELS

Zhi-Dong Bai and Feifang Hu

This paper studies a very general urn model stimulated by designs in 
clinical
trials, where the number of balls of different types added to the urn 
at trial
n depends on a random outcome directed by the composition at trials
1,2,...,n-1. Patient treatments are allocated according to types of 
balls. We
establish the strong consistency and asymptotic normality for both the 
urn
composition and the patient allocation under general assumptions on 
random
generating matrices which determine how balls are added to the urn. 
Also we
obtain explicit forms of the asymptotic variance-covariance matrices of 
both
the urn composition and the patient allocation. The conditions on the
nonhomogeneity of generating matrices are mild and widely satisfied in
applications. Several applications are also discussed.


http://front.math.ucdavis.edu/math.PR/0503521

---------------------------------------------------------------

3224. A BERRY-ESSEEN THEOREM FOR FEYNMAN-KAC AND INTERACTING PARTICLE 
MODELS

Pierre Del Moral and Samy Tindel

In this paper we investigate the speed of convergence of the 
fluctuations of
a general class of Feynman-Kac particle approximation models. We design 
an
original approach based on new Berry-Esseen type estimates for abstract
martingale sequences combined with original exponential concentration 
estimates
of interacting processes. These results extend the corresponding 
statements in
the classical theory and apply to a class of branching and genealogical
path-particle models arising in nonlinear filtering literature as well 
as in
statistical physics and biology.


http://front.math.ucdavis.edu/math.PR/0503522

---------------------------------------------------------------

3225. PERIODIC COPOLYMERS AT SELECTIVE INTERFACES: A LARGE DEVIATIONS 
APPROACH

Erwin Bolthausen and Giambattista Giacomin

We analyze a (1+1)-dimension directed random walk model of a polymer 
dipped
in a medium constituted by two immiscible solvents separated by a flat
interface. The polymer chain is heterogeneous in the sense that a single
monomer may energetically favor one or the other solvent. We focus on 
the case
in which the polymer types are periodically distributed along the chain 
or, in
other words, the polymer is constituted of identical stretches of fixed 
length.
The phenomenon that one wants to analyze is the localization at the 
interface:
energetically favored configurations place most of the monomers in the
preferred solvent and this can be done only if the polymer sticks close 
to the
interface. We investigate, by means of large deviations, the 
energy-entropy
competition that may lead, according to the value of the parameters (the
strength of the coupling between monomers and solvents and an asymmetry
parameter), to localization. We express the free energy of the system 
in terms
of a variational formula that we can solve. We then use the result to 
analyze
the phase diagram.


http://front.math.ucdavis.edu/math.PR/0503523

---------------------------------------------------------------

3226. HITTING DISTRIBUTIONS OF GEOMETRIC BROWNIAN MOTION

T. Byczkowski and M. Ryznar

Let $\tau$ be the first hitting time of the point 1 by the geometric 
Brownian
motion $X(t)= x \exp(B(t)-2\mu t)$ with drift $\mu \geq 0$ starting 
from $x>1$.
Here $B(t)$ is the Brownian motion starting from 0 with $E^0 B^2(t) = 
2t$. We
provide an integral formula for the density function of the stopped 
exponential
functional $A(\tau)=\int_0^\tau X^2(t) dt$ and determine its asymptotic
behaviour at infinity. Although we basically rely on methods developed 
in
\cite{BGS}, the present paper also covers the case of arbitrary drifts 
$\mu
\geq 0$ and provides a significant unification and extension of results 
of the
above-mentioned paper. As a corollary we provide an integral formula 
and give
asymptotic behaviour at infinity of the Poisson kernel for half-spaces 
for
Brownian motion with drift in real hyperbolic spaces of arbitrary 
dimension.


http://front.math.ucdavis.edu/math.PR/0503060

---------------------------------------------------------------

3227. MASS EXTINCTIONS: AN ALTERNATIVE TO THE ALLEE EFFECT

Rinaldo B. Schinazi

We introduce a spatial stochastic process on the lattice Z^d to model 
mass
extinctions. Each site of the lattice may host a flock of up to N 
individuals.
Each individual may give birth to a new individual at the same site at 
rate
\phi until the maximum of N individuals has been reached at the site. 
Once the
flock reaches N individuals, then, and only then, it starts giving 
birth on
each of the 2d neighboring sites at rate \lambda(N). Finally, disaster 
strikes
at rate 1, that is, the whole flock disappears. Our model shows that, 
at least
in theory, there is a critical maximum flock size above which a species 
is
certain to disappear and below which it may survive.


http://front.math.ucdavis.edu/math.PR/0503525

---------------------------------------------------------------

3228. TAIL OF A LINEAR DIFFUSION WITH MARKOV SWITCHING

Benoite de Saporta and Jian-Feng Yao

Let Y be an Ornstein-Uhlenbeck diffusion governed by a stationary and 
ergodic
Markov jump process X: dY_t=a(X_t)Y_t dt+\sigma(X_t) dW_t, Y_0=y_0. 
Ergodicity
conditions for Y have been obtained. Here we investigate the tail 
propriety of
the stationary distribution of this model. A characterization of either 
heavy
or light tail case is established. The method is based on a renewal 
theorem for
systems of equations with distributions on R.


http://front.math.ucdavis.edu/math.PR/0503527

---------------------------------------------------------------

3229. THE LONG-RUN BEHAVIOR OF THE STOCHASTIC REPLICATOR DYNAMICS

Lorens A. Imhof

Fudenberg and Harris' stochastic version of the classical replicator 
dynamics
is considered. The behavior of this diffusion process in the presence 
of an
evolutionarily stable strategy is investigated. Moreover, extinction of
dominated strategies and stochastic stability of strict Nash equilibria 
are
studied. The general results are illustrated in connection with a 
discrete war
of attrition. A persistence result for the maximum effort strategy is 
obtained
and an explicit expression for the evolutionarily stable strategy is 
derived.


http://front.math.ucdavis.edu/math.PR/0503529

---------------------------------------------------------------

3230. OPTIMAL POINTWISE APPROXIMATION OF SDES BASED ON BROWNIAN MOTION 
AT  DISCRETE POINTS

Thomas Muller-Gronbach

We study pathwise approximation of scalar stochastic differential 
equations
at a single point. We provide the exact rate of convergence of the 
minimal
errors that can be achieved by arbitrary numerical methods that are 
based (in a
measurable way) on a finite number of sequential observations of the 
driving
Brownian motion. The resulting lower error bounds hold in particular 
for all
methods that are implementable on a computer and use a random number 
generator
to simulate the driving Brownian motion at finitely many points. Our 
analysis
shows that approximation at a single point is strongly connected to an
integration problem for the driving Brownian motion with a random 
weight.
Exploiting general ideas from estimation of weighted integrals of 
stochastic
processes, we introduce an adaptive scheme, which is easy to implement 
and
performs asymptotically optimally.


http://front.math.ucdavis.edu/math.PR/0503531

---------------------------------------------------------------

3231. QUANTITATIVE BOUNDS ON CONVERGENCE OF TIME-INHOMOGENEOUS MARKOV 
CHAINS

R. Douc and  E. Moulines and Jeffrey S. Rosenthal

Convergence rates of Markov chains have been widely studied in recent 
years.
In particular, quantitative bounds on convergence rates have been 
studied in
various forms by Meyn and Tweedie [Ann. Appl. Probab. 4 (1994) 
981-1101],
Rosenthal [J. Amer. Statist. Assoc. 90 (1995) 558-566], Roberts and 
Tweedie
[Stochastic Process. Appl. 80 (1999) 211-229], Jones and Hobert 
[Statist. Sci.
16 (2001) 312-334] and Fort [Ph.D. thesis (2001) Univ. Paris VI]. In 
this
paper, we extend a result of Rosenthal [J. Amer. Statist. Assoc. 90 
(1995)
558-566] that concerns quantitative convergence rates for 
time-homogeneous
Markov chains. Our extension allows us to consider f-total variation 
distance
(instead of total variation) and time-inhomogeneous Markov chains. We 
apply our
results to simulated annealing.


http://front.math.ucdavis.edu/math.PR/0503532

---------------------------------------------------------------

3232. ON STATIONARITY OF LAGRANGIAN OBSERVATIONS OF PASSIVE TRACER 
VELOCITY IN  A COMPRESSIBLE ENVIRONMENT

Tomasz Komorowski and Grzegorz Krupa

We study the transport of a passive tracer particle in a steady strongly
mixing flow with a nonzero mean velocity. We show that there exists a
probability measure under which the particle Lagrangian velocity 
process is
stationary. This measure is absolutely continuous with respect to the
underlying probability measure for the Eulerian flow.


http://front.math.ucdavis.edu/math.PR/0503534

---------------------------------------------------------------

3233. EXTENDING CHACON-WALSH: MINIMALITY AND GENERALISED STARTING  
DISTRIBUTIONS

Alexander Cox

In this paper we consider the Skorokhod embedding problem for general
starting and target measures. In particular, we provide necessary and
sufficient conditions for a stopping time to be minimal in the sense of
Monroe(1972). The resulting conditions have a nice interpretation in the
graphical picture of Chacon and Walsh. Further, we demonstrate how the
construction of Chacon and Walsh can be extended to any (integrable) 
starting
and target distributions, allowing the constructions of Azema-Yor, 
Vallois and
Jacka to be viewed in this context, and thus extended easily to general
starting and target distributions. In particular, we describe in detail 
the
extension of the Azema-Yor embedding in this context, and show that it 
retains
its optimality property.


http://front.math.ucdavis.edu/math.PR/0503535

---------------------------------------------------------------

3234. EXPONENTIAL PENALTY FUNCTION CONTROL OF LOSS NETWORKS

Garud Iyengar and Karl Sigman

We introduce penalty-function-based admission control policies to
approximately maximize the expected reward rate in a loss network. These
control policies are easy to implement and perform well both in the 
transient
period as well as in steady state. A major advantage of the penalty 
approach is
that it avoids solving the associated dynamic program. However, a 
disadvantage
of this approach is that it requires the capacity requested by 
individual
requests to be sufficiently small compared to total available capacity. 
We
first solve a related deterministic linear program (LP) and then 
translate an
optimal solution of the LP into an admission control policy for the loss
network via an exponential penalty function. We show that the penalty 
policy is
a target-tracking policy--it performs well because the optimal solution 
of the
LP is a good target. We demonstrate that the penalty approach can be 
extended
to track arbitrarily defined target sets. Results from preliminary 
simulation
studies are included.


http://front.math.ucdavis.edu/math.PR/0503536

---------------------------------------------------------------

3235. ELEMENTARY BOUNDS ON POINCARE AND LOG-SOBOLEV CONSTANTS FOR 
DECOMPOSABLE  MARKOV CHAINS

Mark Jerrum and  Jung-Bae Son and  Prasad Tetali and Eric Vigoda

We consider finite-state Markov chains that can be naturally decomposed 
into
smaller ``projection'' and ``restriction'' chains. Possibly this 
decomposition
will be inductive, in that the restriction chains will be smaller 
copies of the
initial chain. We provide expressions for Poincare (resp. log-Sobolev)
constants of the initial Markov chain in terms of Poincare (resp. 
log-Sobolev)
constants of the projection and restriction chains, together with 
further a
parameter. In the case of the Poincare constant, our bound is always at 
least
as good as existing ones and, depending on the value of the extra 
parameter,
may be much better. There appears to be no previously published 
decomposition
result for the log-Sobolev constant. Our proofs are elementary and
self-contained.


http://front.math.ucdavis.edu/math.PR/0503537

---------------------------------------------------------------

3236. RUIN PROBABILITIES AND OVERSHOOTS FOR GENERAL LEVY INSURANCE RISK 
  PROCESSES

Claudia Kluppelberg and  Andreas E. Kyprianou and Ross A. Maller

We formulate the insurance risk process in a general Levy process 
setting,
and give general theorems for the ruin probability and the asymptotic
distribution of the overshoot of the process above a high level, when 
the
process drifts to -\infty a.s. and the positive tail of the Levy 
measure, or of
the ladder height measure, is subexponential or, more generally, 
convolution
equivalent. Results of Asmussen and Kluppelberg [Stochastic Process. 
Appl. 64
(1996) 103-125] and Bertoin and Doney [Adv. in Appl. Probab. 28 (1996) 
207-226]
for ruin probabilities and the overshoot in random walk and compound 
Poisson
models are shown to have analogues in the general setup. The identities 
we
derive open the way to further investigation of general renewal-type 
properties
of Levy processes.


http://front.math.ucdavis.edu/math.PR/0503539

---------------------------------------------------------------

3237. COMBINATORIAL ASPECTS OF MATRIX MODELS

Alice Guionnet and \'Edouard Maurel-Segala

We show that under reasonably general assumptions, the first order
asymptotics of the free energy of matrix models are generating 
functions for
colored planar maps. This is based on the fact that solutions of the
differential Schwinger-Dyson equations are, by nature, generating 
functions for
enumerating planar maps, a remark which bypasses the use of Gaussian 
calculus.


http://front.math.ucdavis.edu/math.PR/0503064

---------------------------------------------------------------

3238. STABILITY IN DISTRIBUTION OF RANDOMLY PERTURBED QUADRATIC MAPS AS 
MARKOV  PROCESSES

Rabi Bhattacharya and Mukul Majumdar

Iteration of randomly chosen quadratic maps defines a Markov process:
X_{n+1}=\epsilon_{n+1}X_n(1-X_n), where \epsilon_n are i.i.d. with 
values in
the parameter space [0,4] of quadratic maps F_{\theta}(x)=\theta 
x(1-x). Its
study is of significance as an important Markov model, with 
applications to
problems of optimization under uncertainty arising in economics. In this
article a broad criterion is established for positive Harris recurrence 
of X_n.


http://front.math.ucdavis.edu/math.PR/0503540

---------------------------------------------------------------

3239. INTERPLAY BETWEEN DIVIDEND RATE AND BUSINESS CONSTRAINTS FOR A 
FINANCIAL  CORPORATION

Tahir Choulli and  Michael Taksar and Xun Yu Zhou

We study a model of a corporation which has the possibility to choose 
various
production/business policies with different expected profits and risks. 
In the
model there are restrictions on the dividend distribution rates as well 
as
restrictions on the risk the company can undertake. The objective is to
maximize the expected present value of the total dividend 
distributions. We
outline the corresponding Hamilton-Jacobi-Bellman equation, compute 
explicitly
the optimal return function and determine the optimal policy. As a 
consequence
of these results, the way the dividend rate and business constraints 
affect the
optimal policy is revealed. In particular, we show that under certain
relationships between the constraints and the exogenous parameters of 
the
random processes that govern the returns, some business activities 
might be
redundant, that is, under the optimal policy they will never be used in 
any
scenario.


http://front.math.ucdavis.edu/math.PR/0503541

---------------------------------------------------------------

3240. LIMIT THEOREMS FOR MIXED MAX-SUM PROCESSES WITH RENEWAL STOPPING

Dmitrii S. Silvestrov and Jozef L. Teugels

This article is devoted to the investigation of limit theorems for mixed
max-sum processes with renewal type stopping indexes. Limit theorems of 
weak
convergence type are obtained as well as functional limit theorems.


http://front.math.ucdavis.edu/math.PR/0503543

---------------------------------------------------------------

3241. CONTINUUM PERCOLATION WITH STEPS IN AN ANNULUS

Paul Balister and  Bela Bollobas and Mark Walters

Let A be the annulus in R^2 centered at the origin with inner and outer 
radii
r(1-\epsilon) and r, respectively. Place points {x_i} in R^2 according 
to a
Poisson process with intensity 1 and let G_A be the random graph with 
vertex
set {x_i} and edges x_ix_j whenever x_i-x_j\in A. We show that if the 
area of A
is large, then G_A almost surely has an infinite component. Moreover, 
if we fix
\epsilon, increase r and let n_c=n_c(\epsilon) be the area of A when 
this
infinite component appears, then n_c\to1 as \epsilon \to 0. This is in 
contrast
to the case of a ``square'' annulus where we show that n_c is bounded 
away from
1.


http://front.math.ucdavis.edu/math.PR/0503544

---------------------------------------------------------------

3242. A MICROSCOPIC PROBABILISTIC DESCRIPTION OF A LOCALLY REGULATED  
POPULATION AND MACROSCOPIC APPROXIMATIONS

Nicolas Fournier and Sylvie Meleard

We consider a discrete model that describes a locally regulated spatial
population with mortality selection. This model was studied in parallel 
by
Bolker and Pacala and Dieckmann, Law and Murrell. We first generalize 
this
model by adding spatial dependence. Then we give a pathwise description 
in
terms of Poisson point measures. We show that different normalizations 
may lead
to different macroscopic approximations of this model. The first 
approximation
is deterministic and gives a rigorous sense to the number density. The 
second
approximation is a superprocess previously studied by Etheridge. 
Finally, we
study in specific cases the long time behavior of the system and of its
deterministic approximation.


http://front.math.ucdavis.edu/math.PR/0503546

---------------------------------------------------------------

3243. STABILITY AND THE LYAPOUNOV EXPONENT OF THRESHOLD AR-ARCH MODELS

Daren B. H. Cline and Huay-min H. Pu

The Lyapounov exponent and sharp conditions for geometric ergodicity are
determined of a time series model with both a threshold autoregression 
term and
threshold autoregressive conditional heteroscedastic (ARCH) errors.
  The conditions require studying or simulating the behavior of a 
bounded,
ergodic Markov chain. The method of proof is based on a new approach, 
called
the piggyback method, that exploits the relationship between the time 
series
and the bounded chain. The piggyback method also provides a means for
evaluating the Lyapounov exponent by simulation and provides a new 
perspective
on moments, illuminating recent results for the distribution tails of 
GARCH
models.


http://front.math.ucdavis.edu/math.PR/0503547

---------------------------------------------------------------

3244. NORMAL APPROXIMATION FOR HIERARCHICAL STRUCTURES

Larry Goldstein

Given F:[a,b]^k\to [a,b] and a nonconstant X_0 with P(X_0\in [a,b])=1, 
define
the hierarchical sequence of random variables {X_n}_{n\ge 0} by
X_{n+1}=F(X_{n,1},...,X_{n,k}), where X_{n,i} are i.i.d. as X_n. Such 
sequences
arise from hierarchical structures which have been extensively studied 
in the
physics literature to model, for example, the conductivity of a random 
medium.
Under an averaging and smoothness condition on nontrivial F, an upper 
bound of
the form C\gamma^n for 0<\gamma<1 is obtained on the Wasserstein 
distance
between the standardized distribution of X_n and the normal. The 
results apply,
for instance, to random resistor networks and, introducing the notion 
of strict
averaging, to hierarchical sequences generated by certain compositions. 
As an
illustration, upper bounds on the rate of convergence to the normal are 
derived
for the hierarchical sequence generated by the weighted diamond lattice 
which
is shown to exhibit a full range of convergence rate behavior.


http://front.math.ucdavis.edu/math.PR/0503549

---------------------------------------------------------------

3245. ON THE SUPER REPLICATION PRICE OF UNBOUNDED CLAIMS

Sara Biagini and Marco Frittelli

In an incomplete market the price of a claim f in general cannot be 
uniquely
identified by no arbitrage arguments. However, the ``classical'' super
replication price is a sensible indicator of the (maximum selling) 
value of the
claim. When f satisfies certain pointwise conditions (e.g., f is 
bounded from
below), the super replication price is equal to sup_QE_Q[f], where Q 
varies on
the whole set of pricing measures. Unfortunately, this price is often 
too high:
a typical situation is here discussed in the examples. We thus define 
the less
expensive weak super replication price and we relax the requirements on 
f by
asking just for ``enough'' integrability conditions. By building up a 
proper
duality theory, we show its economic meaning and its relation with the
investor's preferences. Indeed, it turns out that the weak super 
replication
price of f coincides with sup_{Q\in M_{\Phi}}E_Q[f], where M_{\Phi} is 
the
class of pricing measures with finite generalized entropy (i.e., E[\Phi
(\frac{dQ}{dP})]<\infty) and where \Phi is the convex conjugate of the 
utility
function of the investor.


http://front.math.ucdavis.edu/math.PR/0503550

---------------------------------------------------------------

3246. LIMIT LAWS OF ESTIMATORS FOR CRITICAL MULTI-TYPE GALTON-WATSON 
PROCESSES

Zhiyi Chi

We consider the asymptotics of various estimators based on a large 
sample of
branching trees from a critical multi-type Galton-Watson process, as 
the sample
size increases to infinity. The asymptotics of additive functions of 
trees,
such as sizes of trees and frequencies of types within trees, a 
higher-order
asymptotic of the ``relative frequency'' estimator of the left 
eigenvector of
the mean matrix, a higher-order joint asymptotic of the maximum 
likelihood
estimators of the offspring probabilities and the consistency of an 
estimator
of the right eigenvector of the mean matrix, are established.


http://front.math.ucdavis.edu/math.PR/0503552

---------------------------------------------------------------

3247. ON SAMPLING OF STATIONARY INCREMENT PROCESSES

J. M. P. Albin

Under a complex technical condition, similar to such used in extreme 
value
theory, we find the rate q(\epsilon)^{-1} at which a stochastic process 
with
stationary increments \xi should be sampled, for the sampled process
\xi(\lfloor\cdot /q(\epsilon)\rfloor q(\epsilon)) to deviate from \xi 
by at
most \epsilon, with a given probability, asymptotically as \epsilon
\downarrow0. The canonical application is to discretization errors in 
computer
simulation of stochastic processes.


http://front.math.ucdavis.edu/math.PR/0503554

---------------------------------------------------------------

3248. RECURRENCE OF SIMPLE RANDOM WALK ON $Z^2$ IS DYNAMICALLY SENSITIVE

Christopher Hoffman

Benjamini, Haggstrom, Peres and Steif introduced the concept of a 
dynamical
random walk. This is a continuous family of random walks, {S_n(t)}. 
Benjamini
et. al. proved that if d=3 or d=4 then there is an exceptional set of t 
such
that {S_n(t)} returns to the origin infinitely often. In this paper we 
consider
a dynamical random walk on Z^2. We show that with probability one there 
exists
t such that {S_n(t)} never returns to the origin. This exceptional set 
of times
has dimension one. This proves a conjecture of Benjamini et. al.


http://front.math.ucdavis.edu/math.PR/0503065

---------------------------------------------------------------

3249. SPECTRAL PROPERTIES OF THE TANDEM JACKSON NETWORK, SEEN AS A  
QUASI-BIRTH-AND-DEATH PROCESS

D. P. Kroese and  W. R. W. Scheinhardt and P. G. Taylor

Quasi-birth-and-death (QBD) processes with infinite ``phase spaces'' can
exhibit unusual and interesting behavior. One of the simplest examples 
of such
a process is the two-node tandem Jackson network, with the ``phase'' 
giving the
state of the first queue and the ``level'' giving the state of the 
second
queue. In this paper, we undertake an extensive analysis of the 
properties of
this QBD. In particular, we investigate the spectral properties of 
Neuts's
R-matrix and show that the decay rate of the stationary distribution of 
the
``level'' process is not always equal to the convergence norm of R. In 
fact, we
show that we can obtain any decay rate from a certain range by 
controlling only
the transition structure at level zero, which is independent of R. We 
also
consider the sequence of tandem queues that is constructed by 
restricting the
waiting room of the first queue to some finite capacity, and then 
allowing this
capacity to increase to infinity. We show that the decay rates for the 
finite
truncations converge to a value, which is not necessarily the decay 
rate in the
infinite waiting room case. Finally, we show that the probability that 
the
process hits level n before level 0 given that it starts in level 1 
decays at a
rate which is not necessarily the same as the decay rate for the 
stationary
distribution.


http://front.math.ucdavis.edu/math.PR/0503555

---------------------------------------------------------------

3250. NUMBER OF PATHS VERSUS NUMBER OF BASIS FUNCTIONS IN AMERICAN 
OPTION  PRICING

Paul Glasserman and Bin Yu

An American option grants the holder the right to select the time at 
which to
exercise the option, so pricing an American option entails solving an 
optimal
stopping problem. Difficulties in applying standard numerical methods to
complex pricing problems have motivated the development of techniques 
that
combine Monte Carlo simulation with dynamic programming. One class of 
methods
approximates the option value at each time using a linear combination 
of basis
functions, and combines Monte Carlo with backward induction to estimate 
optimal
coefficients in each approximation. We analyze the convergence of such 
a method
as both the number of basis functions and the number of simulated paths
increase. We get explicit results when the basis functions are 
polynomials and
the underlying process is either Brownian motion or geometric Brownian 
motion.
We show that the number of paths required for worst-case convergence 
grows
exponentially in the degree of the approximating polynomials in the 
case of
Brownian motion and faster in the case of geometric Brownian motion.


http://front.math.ucdavis.edu/math.PR/0503556

---------------------------------------------------------------

3251. STOCHASTIC CHARACTERIZATION OF HARMONIC MAPS ON RIEMANNIAN 
POLYHEDRA

M. A. Aprodu and  T. Bouziane

The aim of this paper is to relate the theory of Harmonicity in sense
Korevaar-Schoen and Eells-Fuglede to the notion of a Brownian motion in
riemannian polyhedra achieved by the second author. Firstly, we prove 
that
Brownian motions is stochastically continuous Markov processes and 
consequently
it has a unique infinitesimal generator on some Banach space. Secondly, 
we show
that in some sense, the Brownian motion in Riemannian polyhedra has as 
an
infinitesimal generator the "Laplacian". Finally, we show that harmonic 
maps,
with target smooth Riemannian manifolds, in the sense of Eells-Fuglede, 
are
exactly those which maps Brownian motion in Riemannian polyhedron into a
martingale, while harmonic morphisms are exactly the maps which are 
Brownian
preserving paths


http://front.math.ucdavis.edu/math.PR/0503557

---------------------------------------------------------------

3252. CENTRAL LIMIT THEOREMS FOR RANDOM POLYTOPES IN A SMOOTH CONVEX SET

Van Vu

Let $K$ be a smooth convex set with volume one in $\BBR^d$. Choose $n$ 
random
points in $K$ independently according to the uniform distribution. The 
convex
hull of these points, denoted by $K_n$, is called a {\it random 
polytope}. We
prove that several key functionals of $K_n$ satisfy the central limit 
theorem
as $n$ tends to infinity.


http://front.math.ucdavis.edu/math.PR/0503559

---------------------------------------------------------------

3253. QUENCHED INVARIANCE PRINCIPLE FOR SIMPLE RANDOM WALK ON 
TWO-DIMENSIONAL  PERCOLATION CLUSTERS

Noam Berger and Marek Biskup

We consider the simple random walk on a two-dimensional super-critical
infinite percolation cluster and prove that for almost every 
configuration it
scales to Brownian motion.


http://front.math.ucdavis.edu/math.PR/0503576

---------------------------------------------------------------

3254. ASYMPTOTIC GENEALOGY OF A CRITICAL BRANCHING PROCESS

Lea Popovic

Consider a continuous-time binary branching process conditioned to have
population size n at some time t, and with a chance p for recording each
extinct individual in the process. Within the family tree of this 
process, we
consider the smallest subtree containing the genealogy of the extant
individuals together with the genealogy of the recorded extinct 
individuals. We
introduce a novel representation of such subtrees in terms of a 
point-process,
and provide asymptotic results on the distribution of this 
point-process as the
number of extant individuals increases. We motivate the study within 
the scope
of a coherent analysis for an a priori model for macroevolution.


http://front.math.ucdavis.edu/math.PR/0503577

---------------------------------------------------------------

3255. GENERALIZED STOCHASTIC DIFFERENTIAL UTILITY AND PREFERENCE FOR  
INFORMATION

Ali Lazrak

This paper develops, in a Brownian information setting, an approach for
analyzing the preference for information, a question that motivates the
stochastic differential utility (SDU) due to Duffie and Epstein 
[Econometrica
60 (1992) 353-394]. For a class of backward stochastic differential 
equations
(BSDEs) including the generalized SDU [Lazrak and Quenez Math. Oper. 
Res. 28
(2003) 154-180], we formulate the information neutrality property as an
invariance principle when the filtration is coarser (or finer) and 
characterize
it. We also provide concrete examples of heterogeneity in information 
that
illustrate explicitly the nonneutrality property for some GSDUs. Our 
results
suggest that, within the GSDUs class of intertemporal utilities, risk 
aversion
or ambiguity aversion are inflexibly linked to the preference for 
information.


http://front.math.ucdavis.edu/math.PR/0503579

---------------------------------------------------------------

3256. THE RIGHT TIME TO SELL A STOCK WHOSE PRICE IS DRIVEN BY MARKOVIAN 
NOISE

Robert C. Dalang and M.-O. Hongler

We consider the problem of finding the optimal time to sell a stock, 
subject
to a fixed sales cost and an exponential discounting rate \rho. We 
assume that
the price of the stock fluctuates according to the equation dY_t=Y_t(\mu
dt+\sigma\xi(t) dt), where (\xi(t)) is an alternating Markov renewal 
process
with values in {\pm1}, with an exponential renewal time. We determine 
the
critical value of \rho under which the value function is finite. We 
examine the
validity of the ``principle of smooth fit'' and use this to give a 
complete and
essentially explicit solution to the problem, which exhibits a 
surprisingly
rich structure. The corresponding result when the stock price evolves 
according
to the Black and Scholes model is obtained as a limit case.


http://front.math.ucdavis.edu/math.PR/0503580

---------------------------------------------------------------

3257. CONCENTRATION OF NORMALIZED SUMS AND A CENTRAL LIMIT THEOREM FOR  
NONCORRELATED RANDOM VARIABLES

Sergey G. Bobkov

For noncorrelated random variables, we study a concentration property 
of the
family of distributions of normalized sums formed by sequences of times 
of a
given large length.


http://front.math.ucdavis.edu/math.PR/0503583

---------------------------------------------------------------

3258. ANALYSIS OF A CLASS OF LIKELIHOOD BASED CONTINUOUS TIME 
STOCHASTIC  VOLATILITY MODELS INCLUDING ORNSTEIN-UHLENBECK MODELS IN 
FINANCIAL ECONOMICS

Lancelot F. James

In a series of recent papers Barndorff-Nielsen and Shephard introduce an
attractive class of continuous time stochastic volatility models for 
financial
assets where the volatility processes are functions of positive
Ornstein-Uhlenbeck(OU) processes. This models are known to be 
substantially
more flexible than Gaussian based models. One current problem of this 
approach
is the unavailability of a tractable exact analysis of likelihood based
stochastic volatility models for the returns of log prices of stocks.
   With this point in mind, the likelihood models of Barndorff-Nielsen 
and
Shephard are viewed as members of a much larger class of models. That is
likelihoods based on n conditionally independent Normal random 
variables whose
mean and variance are representable as linear functionals of a common
unobserved Poisson random measure. The analysis of these models is 
facilitated
by applying the methods in James (2005, 2002), in particular an Esscher 
type
transform of Poisson random measures; in conjunction with a special 
case of the
Weber-Sonine formula. It is shown that the marginal likelihood may be 
expressed
in terms of a multidimensional Fourier-cosine transform. This yields 
tractable
forms of the likelihood and also allows a full Bayesian posterior 
analysis of
the integrated volatility process. A general formula for the posterior 
density
of the log price given the observed data is derived, which could 
potentially
have applications to option pricing. We also identify tractable 
subclasses,
where inference can be based on a finite number of independent random
variables. It is shown that inference does not necessarily require 
simulation
of random measures. Rather, classical numerical integration can be used 
in the
most general cases.


http://front.math.ucdavis.edu/math.ST/0503055

---------------------------------------------------------------

3259. MODIFIED LOGARITHMIC SOBOLEV INEQUALITIES IN NULL CURVATURE

Ivan Gentil and  Arnaud Guillin and Laurent Miclo

We present a logarithmic Sobolev inequality adapted to a log-concave 
measure.
Assume that $\Phi$ is a symmetric convex function on $\dR$ satisfying
$(1+\e)\Phi(x)\leq {x}\Phi'(x)\leq(2-\e)\Phi(x)$ for $x\geq0$ large 
enough and
with $\e\in]0,1/2]$. We prove that the probability measure on $\dR$
$\mu_\Phi(dx)=e^{-\Phi(x)}/Z_\Phi dx$ satisfies a modified and adapted
logarithmic Sobolev inequality : there exist three constant $A,B,D>0$ 
such that
for all smooth $f>0$, \begin{equation*}
   \ent{\mu_\Phi}{f^2}\leq A\int 
H_{\Phi}\PAR{{\frac{f'}{f}}}f^2d\mu_\Phi,
\text{with} H_{\Phi}(x)= {\begin{array}{rl} \Phi^*\PAR{Bx} &\text{if
}\ABS{x}\geq D, x^2 &\text{if}\ABS{x}\leq D. \end{array} . 
\end{equation*}


http://front.math.ucdavis.edu/math.PR/0503585

---------------------------------------------------------------

3260. LENSES IN SKEW BROWNIAN FLOW

Krzysztof Burdzy and Haya Kaspi

We consider a stochastic flow in which individual particles follow skew
Brownian motions, with each one of these processes driven by the same 
Brownian
motion. One does not have uniqueness for the solutions of the 
corresponding
stochastic differential equation simultaneously for all real initial
conditions. Due to this lack of the simultaneous strong uniqueness for 
the
whole system of stochastic differential equations, the flow contains 
lenses,
that is, pairs of skew Brownian motions which start at the same point,
bifurcate, and then coalesce in a finite time. The paper contains 
qualitative
and quantitative (distributional) results on the geometry of the flow 
and
lenses.


http://front.math.ucdavis.edu/math.PR/0503586

---------------------------------------------------------------

3261. WEAK POINCARE INEQUALITIES ON DOMAINS DEFINED BY BROWNIAN ROUGH 
PATHS

Shigeki Aida

We prove weak Poincare inequalities on domains which are inverse images 
of
open sets in Wiener spaces under continuous functions of Brownian rough 
paths.
The result is applicable to Dirichlet forms on loop groups and 
connected open
subsets of path spaces over compact Riemannian manifolds.


http://front.math.ucdavis.edu/math.PR/0503587

---------------------------------------------------------------

3262. TIME CHANGES OF SYMMETRIC DIFFUSIONS AND FELLER MEASURES

Masatoshi Fukushima and  Ping He and Jiangang Ying

We extend the classical Douglas integral, which expresses the Dirichlet
integral of a harmonic function on the unit disk in terms of its value 
on
boundary, to the case of conservative symmetric diffusion in terms of 
Feller
measure, by using the approach of time change of Markov processes.


http://front.math.ucdavis.edu/math.PR/0503588

---------------------------------------------------------------

3263. DIFFERENCE PROPHET INEQUALITIES FOR [0,1]-VALUED I.I.D. RANDOM 
VARIABLES  WITH COST FOR OBSERVATIONS

Holger Kosters

Let X_1,X_2,... be a sequence of [0,1]-valued i.i.d. random variables, 
let
c\geq 0 be a sampling cost for each observation and let Y_i=X_i-ic, 
i=1,2,....
For n=1,2,..., let M(Y_1,...,Y_n)=E(max_{1\leq i\leq n}Y_i) and
V(Y_1,...,Y_n)=sup_{\tau \in C^n}E(Y_{\tau}), where C^n denotes the set 
of all
stopping rules for Y_1,...,Y_n. Sharp upper bounds for the difference
M(Y_1,...,Y_n)-V(Y_1,...,Y_n) are given under various restrictions on c 
and n.


http://front.math.ucdavis.edu/math.PR/0503589

---------------------------------------------------------------

3264. UNIQUENESS FOR DIFFUSIONS DEGENERATING AT THE BOUNDARY OF A 
SMOOTH  BOUNDED SET

Dante DeBlassie

For continuous \gamma, g:[0,1]\to(0,\infty), consider the degenerate
stochastic differential equation dX_t=[1-|X_t|^2]^{1/2}\gamma(|X_t|)
dB_t-g(|X_t|)X_t dt in the closed unit ball of R^n. We introduce a new 
idea to
show pathwise uniqueness holds when \gamma and g are Lipschitz and
\frac{g(1)}{\gamma^2(1)}>\sqrt2-1. When specialized to a case studied 
by Swart
[Stochastic Process. Appl. 98 (2002) 131-149] with \gamma=\sqrt2 and 
g\equiv c,
this gives an improvement of his result. Our method applies to more 
general
contexts as well. Let D be a bounded open set with C^3 boundary and 
suppose
h:\barD\to R Lipschitz on \barD, as well as C^2 on a neighborhood of 
\partial D
with Lipschitz second partials there. Also assume h>0 on D, h=0 on 
\partial D
and |\nabla h|>0 on \partial D. An example of such a function is
h(x)=d(x,\partial D). We give conditions which ensure pathwise 
uniqueness holds
for dX_t=h(X_t)^{1/2}\sigma(X_t) dB_t+b(X_t) dt in \barD.


http://front.math.ucdavis.edu/math.PR/0503590

---------------------------------------------------------------

3265. MODERATE DEVIATIONS FOR DIFFUSIONS WITH BROWNIAN POTENTIALS

Yueyun Hu and Zhan Shi

We present precise moderate deviation probabilities, in both quenched 
and
annealed settings, for a recurrent diffusion process with a Brownian 
potential.
Our method relies on fine tools in stochastic calculus, including 
Kotani's
lemma and Lamperti's representation for exponential functionals. In 
particular,
our result for quenched moderate deviations is in agreement with a 
recent
theorem of Comets and Popov [Probab. Theory Related Fields 126 (2003) 
571-609]
who studied the corresponding problem for Sinai's random walk in random
environment.


http://front.math.ucdavis.edu/math.PR/0503591

---------------------------------------------------------------

3266. SELF-INTERSECTION LOCAL TIME: CRITICAL EXPONENT, LARGE 
DEVIATIONS, AND  LAWS OF THE ITERATED LOGARITHM

Richard F. Bass and Xia Chen

If \beta_t is renormalized self-intersection local time for planar 
Brownian
motion, we characterize when Ee^{\gamma\beta_1} is finite or infinite 
in terms
of the best constant of a Gagliardo-Nirenberg inequality. We prove large
deviation estimates for \beta_1 and -\beta_1. We establish lim sup and 
lim inf
laws of the iterated logarithm for \beta_t as t\to\infty.


http://front.math.ucdavis.edu/math.PR/0503592

---------------------------------------------------------------

3267. EXPONENTIAL ASYMPTOTICS AND LAW OF THE ITERATED LOGARITHM FOR  
INTERSECTION LOCAL TIMES OF RANDOM WALKS

Xia Chen

Let \alpha ([0,1]^p) denote the intersection local time of p independent
d-dimensional Brownian motions running up to the time 1. Under the 
conditions
p(d-2)<d and d\ge 2, we prove lim_{t\to\infty}t^{-1}\log
P\bigl{\alpha([0,1]^p)\ge t^{(d(p-1))/2}\bigr}=-\gamma_{\alpha}(d,p) 
with the
right-hand side being identified in terms of the the best constant of 
the
Gagliardo-Nirenberg inequality. Within the scale of moderate 
deviations, we
also establish the precise tail asymptotics for the intersection local 
time
I_n=#{(k_1,...,k_p)\in [1,n]^p;S_1(k_1)=... =S_p(k_p)} run by the 
independent,
symmetric, Z^d-valued random walks S_1(n),...,S_p(n). Our results apply 
to the
law of the iterated logarithm. Our approach is based on Feynman-Kac 
type large
deviation, time exponentiation, moment computation and some 
technologies along
the lines of probability in Banach space. As an interesting coproduct, 
we
obtain the inequality \bigl(EI_{n_1+... +n_a}^m\bigr)^{1/p}\le 
\sum_{k_1+...
+k_a=m\limits_{k_1,...,k_a\ge 0}}\frac{m!}{k_1!...
k_a!}\bigl(EI_{n_1}^{k_1}\bigr)^{1/p}... 
\bigl(EI_{n_a}^{k_a}\bigr)^{1/p} in
the case of random walks.


http://front.math.ucdavis.edu/math.PR/0503593

---------------------------------------------------------------

3268. REGULARITY OF SOLUTIONS TO STOCHASTIC VOLTERRA EQUATIONS WITH 
INFINITE  DELAY

Anna Karczewska and  Carlos Lizama

The paper gives necessary and sufficient conditions providing 
regularity of
solutions to stochastic Volterra equations with infinite delay on a
$d$-dimensional torus. The harmonic analysis techniques and stochastic
integration in function spaces are used.


http://front.math.ucdavis.edu/math.PR/0503595

---------------------------------------------------------------

3269. A CLASS OF GENERALIZED HYPERBOLIC CONTINUOUS TIME INTEGRATED 
STOCHASTIC  VOLATILITY LIKELIHOOD MODELS

Lancelot F. James and John W. Lau

This paper discusses and analyzes a class of likelihood models which are
based on two distributional innovations in financial models for stock 
returns.
That is, the notion that the marginal distribution of aggregate returns 
of
log-stock prices are well approximated by generalized hyperbolic 
distributions,
and that volatility clustering can be handled by specifying the 
integrated
volatility as a random process such as that proposed in a recent series 
of
papers by Barndorff-Nielsen and Shephard (BNS). The BNS models produce
likelihoods for aggregate returns which can be viewed as a subclass of 
latent
regression models where one has n conditionally independent Normal 
random
variables whose mean and variance are representable as linear 
functionals of a
common unobserved Poisson random measure. James (2005b) recently 
obtains an
exact analysis for such models yielding expressions of the likelihood 
in terms
of quite tractable Fourier-Cosine integrals. Here, our idea is to 
analyze a
class of likelihoods, which can be used for similar purposes, but where 
the
latent regression models are based on n conditionally independent 
models with
distributions belonging to a subclass of the generalized hyperbolic
distributions and whose corresponding parameters are representable as 
linear
functionals of a common unobserved Poisson random measure. Our models 
are
perhaps most closely related to the Normal inverse 
Gaussian/GARCH/A-PARCH
models of Brandorff-Nielsen (1997) and Jensen and Lunde (2001), where 
in our
case the GARCH component is replaced by quantities such as INT-OU 
processes. It
is seen that, importantly, such likelihood models exhibit quite 
different
features structurally. One nice feature of the model is that it allows 
for more
flexibility in terms of modelling of external regression parameters.


http://front.math.ucdavis.edu/math.ST/0503056

---------------------------------------------------------------

3270. A LOCAL LIMIT THEOREM FOR DIRECTED POLYMERS IN RANDOM MEDIA: THE  
CONTINUOUS AND THE DISCRETE CASE

Vincent Vargas (PMA)

In this article, we consider two models of directed polymers in random
environment: a discrete model and a continuous model. We consider these 
models
in dimension greater or equal to 3 and we suppose that the normalized 
partition
function is bounded in L^2. Under these assumptions, Sinai proved a 
local limit
theorem for the discrete model, using a perturbation expansion. In this
article, we give a new method for proving Sinai's local limit theorem. 
This new
method can be transposed to the continuous setting in which we prove a 
similar
local limit theorem.


http://front.math.ucdavis.edu/math.PR/0503596

---------------------------------------------------------------

3271. GLOBAL L_2-SOLUTIONS OF STOCHASTIC NAVIER-STOKES EQUATIONS

R. Mikulevicius and B. L. Rozovskii

This paper concerns the Cauchy problem in R^d for the stochastic
Navier-Stokes equation \partial_tu=\Delta u-(u,\nabla)u-\nabla p+f(u)+
[(\sigma,\nabla)u-\nabla \tilde p+g(u)]\circ \dot W, u(0)=u_0,\qquad 
divu=0,
driven by white noise \dot W. Under minimal assumptions on regularity 
of the
coefficients and random forces, the existence of a global weak 
(martingale)
solution of the stochastic Navier-Stokes equation is proved. In the
two-dimensional case, the existence and pathwise uniqueness of a global 
strong
solution is shown. A Wiener chaos-based criterion for the existence and
uniqueness of a strong global solution of the Navier-Stokes equations is
established.


http://front.math.ucdavis.edu/math.PR/0503597

---------------------------------------------------------------

3272. CENTRAL LIMIT THEOREMS FOR SEQUENCES OF MULTIPLE STOCHASTIC 
INTEGRALS

David Nualart and Giovanni Peccati

We characterize the convergence in distribution to a standard normal 
law for
a sequence of multiple stochastic integrals of a fixed order with 
variance
converging to 1. Some applications are given, in particular to study the
limiting behavior of quadratic functionals of Gaussian processes.


http://front.math.ucdavis.edu/math.PR/0503598

---------------------------------------------------------------

3273. STOCHASTIC INTEGRAL REPRESENTATION AND REGULARITY OF THE DENSITY 
FOR THE  EXIT MEASURE OF SUPER-BROWNIAN MOTION

Jean-Francois Le Gall and Leonid Mytnik

This paper studies the regularity properties of the density of the exit
measure for super-Brownian motion with (1+\beta)-stable branching 
mechanism. It
establishes the continuity of the density in dimension d=2 and the
unboundedness of the density in all other dimensions where the density 
exists.
An alternative description of the exit measure and its density is also 
given
via a stochastic integral representation. Results are applied to the
probabilistic representation of nonnegative solutions of the partial
differential equation \Delta u=u^{1+\beta}.


http://front.math.ucdavis.edu/math.PR/0503599

---------------------------------------------------------------

3274. PRECISE ASYMPTOTICS OF SMALL EIGENVALUES OF REVERSIBLE DIFFUSIONS 
IN THE  METASTABLE REGIME

Michael Eckhoff

We investigate the close connection between metastability of the 
reversible
diffusion process X defined by the stochastic differential equation
dX_t=-\nabla F(X_t) dt+\sqrt2\epsilon dW_t,\qquad \epsilon >0, and the 
spectrum
near zero of its generator -L_{\epsilon}\equiv \epsilon \Delta -\nabla
F\cdot\nabla, where F:R^d\to R and W denotes Brownian motion on R^d. For
generic F to each local minimum of F there corresponds a metastable 
state. We
prove that the distribution of its rescaled relaxation time converges 
to the
exponential distribution as \epsilon \downarrow 0 with optimal and 
uniform
error estimates. Each metastable state can be viewed as an eigenstate of
L_{\epsilon} with eigenvalue which converges to zero exponentially fast 
in
1/\epsilon. Modulo errors of exponentially small order in 1/\epsilon 
this
eigenvalue is given as the inverse of the expected metastable 
relaxation time.
The eigenstate is highly concentrated in the basin of attraction of the
corresponding trap.


http://front.math.ucdavis.edu/math.PR/0503600

---------------------------------------------------------------

3275. ASYMPTOTIC EXPANSIONS FOR THE LAPLACE APPROXIMATIONS OF SUMS OF 
BANACH  SPACE-VALUED RANDOM VARIABLES

Sergio Albeverio and Song Liang

Let X_i, i\in N, be i.i.d. B-valued random variables, where B is a real
separable Banach space. Let \Phi be a smooth enough mapping from B into 
R. An
asymptotic evaluation of Z_n=E(\exp (n\Phi (\sum_{i=1}^nX_i/n))), up to 
a
factor (1+o(1)), has been gotten in Bolthausen [Probab. Theory Related 
Fields
72 (1986) 305-318] and Kusuoka and Liang [Probab. Theory Related Fields 
116
(2000) 221-238]. In this paper, a detailed asymptotic expansion of Z_n 
as n\to
\infty is given, valid to all orders, and with control on remainders. 
The
results are new even in finite dimensions.


http://front.math.ucdavis.edu/math.PR/0503601

---------------------------------------------------------------

3276. MULTIPLICATIVE MONOTONE CONVOLUTIONS

Uwe Franz

Recently, Bercovici has introduced multiplicative convolutions based on
Muraki's monotone independence and shown that these convolution of 
probability
measures correspond to the composition of some function of their Cauchy
transforms. We provide a new proof of this fact based on the 
combinatorics of
moments. We also give a new characterisation of the probability 
measures that
can be embedded into continuous monotone convolution semigroups of 
probability
measures on the unit circle and briefly discuss a relation to 
Galton-Watson
processes.


http://front.math.ucdavis.edu/math.PR/0503602

---------------------------------------------------------------

3277. EXTREMES ON TREES

Tailen Hsing and Holger Rootzen

This paper considers the asymptotic distribution of the longest edge of 
the
minimal spanning tree and nearest neighbor graph on X_1,...,X_{N_n} 
where
X_1,X_2,... are i.i.d. in \Re^2 with distribution F and N_n is 
independent of
the X_i and satisfies N_n/n\to_p1. A new approach based on spatial 
blocking and
a locally orthogonal coordinate system is developed to treat cases for 
which F
has unbounded support. The general results are applied to a number of 
special
cases, including elliptically contoured distributions, distributions 
with
independent Weibull-like margins and distributions with parallel level 
curves.


http://front.math.ucdavis.edu/math.PR/0503603

---------------------------------------------------------------

3278. ON THE MONOTONICITY OF THE SPEED OF RANDOM WALKS ON A PERCOLATION 
  CLUSTER OF TREES

Dayue Chen and Fuxi Zhang

We consider the simple random walk on the infinite cluster of the 
Bernoulli
bond percolation of trees, and investigate the relation between the 
speed of
the simple random walk and the retaining probability $p$ by studying 
three
classes of trees. A sufficient condition is established for 
Galton-Watson
trees.


http://front.math.ucdavis.edu/math.PR/0503610

---------------------------------------------------------------

3279. CONTRACTIVE MARKOV SYSTEMS II

Ivan Werner

In this paper, we continue development of the theory of contractive 
Markov
systems (CMSs) initiated in \cite{Wer1}. We extend some results from
\cite{Wer1}, \cite{Wer3}, \cite{Wer5} and \cite{Wer6} to the case of
contractive Markov systems with probabilities which have a square 
summable
variation by using some ideas of A. Johansson and A. Oeberg \cite{JO}. 
In
particular, we show that an irreducible CMS has a unique invariant Borel
probability measure if the vertex sets form an open partition of the 
state
space and the restrictions of the probability functions on their vertex 
sets
have a square summable variation and are bounded away from zero.


http://front.math.ucdavis.edu/math.PR/0503633

---------------------------------------------------------------

3280. LIMIT THEOREMS FOR ITERATED RANDOM TOPICAL OPERATORS

Glenn Merlet (IRMAR)

Let A(n) be a sequence of i.i.d. topical (i.e. isotone and additively
homogeneous) operators. Let $x(n,x\_0)$ be defined by $x(0,x\_0)=x\_0$ 
and
$x(n,x\_0)=A(n)x(n-1,x\_0)$. This can modelize a wide range of systems
including, task graphs, train networks, Job-Shop, timed digital 
circuits or
parallel processing systems. When A(n) has the memory loss property, we 
use the
spectral gap method to prove limit theorems for $x(n,x\_0)$. Roughly 
speaking,
we show that $x(n,x\_0)$ behaves like a sum of i.i.d. real variables.
Precisely, we show that with suitable additional conditions, it 
satisfies a
central limit theorem with rate, a local limit theorem, a renewal 
theorem and a
large deviations principle, and we give an algebraic condition to 
ensure the
positivity of the variance in the CLT. When A(n) are defined by 
matrices in the
\mp semi-ring, we give more effective statements and show that the 
additional
conditions and the positivity of the variance in the CLT are generic.


http://front.math.ucdavis.edu/math.PR/0503634

---------------------------------------------------------------

3281. A PROBABILISTIC APPROACH TO THE GEOMETRY OF THE \ELL_P^N-BALL

Franck Barthe and  Olivier Guedon and  Shahar Mendelson and Assaf Naor

This article investigates, by probabilistic methods, various geometric
questions on B_p^n, the unit ball of \ell_p^n. We propose realizations 
in terms
of independent random variables of several distributions on B_p^n, 
including
the normalized volume measure. These representations allow us to unify 
and
extend the known results of the sub-independence of coordinate slabs in 
B_p^n.
As another application, we compute moments of linear functionals on 
B_p^n,
which gives sharp constants in Khinchine's inequalities on B_p^n and 
determines
the \psi_2-constant of all directions on B_p^n. We also study the 
extremal
values of several Gaussian averages on sections of B_p^n (including 
mean width
and \ell-norm), and derive several monotonicity results as p varies.
Applications to balancing vectors in \ell_2 and to covering numbers of
polyhedra complete the exposition.


http://front.math.ucdavis.edu/math.PR/0503650

---------------------------------------------------------------

3282. MOMENT INEQUALITIES FOR FUNCTIONS OF INDEPENDENT RANDOM VARIABLES

Stephane Boucheron and  Olivier Bousquet and  Gabor Lugosi and Pascal 
Massart

A general method for obtaining moment inequalities for functions of
independent random variables is presented. It is a generalization of the
entropy method which has been used to derive concentration inequalities 
for
such functions [Boucheron, Lugosi and Massart Ann. Probab. 31 (2003)
1583-1614], and is based on a generalized tensorization inequality due 
to
Latala and Oleszkiewicz [Lecture Notes in Math. 1745 (2000) 147-168]. 
The new
inequalities prove to be a versatile tool in a wide range of 
applications. We
illustrate the power of the method by showing how it can be used to
effortlessly re-derive classical inequalities including Rosenthal and
Kahane-Khinchine-type inequalities for sums of independent random 
variables,
moment inequalities for suprema of empirical processes and moment 
inequalities
for Rademacher chaos and U-statistics. Some of these corollaries are 
apparently
new. In particular, we generalize Talagrand's exponential inequality for
Rademacher chaos of order 2 to any order. We also discuss applications 
for
other complex functions of independent random variables, such as 
suprema of
Boolean polynomials which include, as special cases, subgraph counting 
problems
in random graphs.


http://front.math.ucdavis.edu/math.PR/0503651

---------------------------------------------------------------

3283. ON THE STOCHASTIC CALCULUS METHOD FOR SPINS SYSTEMS

Samy Tindel

In this note we show how to generalize the stochastic calculus method
introduced by Comets and Neveu [Comm. Math. Phys. 166 (1995) 549-564] 
for two
models of spin glasses, namely, the SK model with external field and the
perceptron model. This method allows to derive quite easily some 
fluctuation
results for the free energy in those two cases.


http://front.math.ucdavis.edu/math.PR/0503652

---------------------------------------------------------------

3284. CLOSURES OF EXPONENTIAL FAMILIES

Imre Csiszar and Frantisek Matus

The variation distance closure of an exponential family with a convex 
set of
canonical parameters is described, assuming no regularity conditions. 
The tools
are the concepts of convex core of a measure and extension of an 
exponential
family, introduced previously by the authors, and a new concept of 
accessible
faces of a convex set. Two other closures related to the information 
divergence
are also characterized.


http://front.math.ucdavis.edu/math.PR/0503653

---------------------------------------------------------------

3285. ONE-DEPENDENT TRIGONOMETRIC DETERMINANTAL PROCESSES ARE  
TWO-BLOCK-FACTORS

Erik I. Broman

Given a trigonometric polynomial f:[0,1]\to[0,1] of degree m, one can 
define
a corresponding stationary process {X_i}_{i\in Z} via determinants of 
the
Toeplitz matrix for f. We show that for m=1 this process, which is 
trivially
one-dependent, is a two-block-factor.


http://front.math.ucdavis.edu/math.PR/0503654

---------------------------------------------------------------

3286. ASYMPTOTICS FOR HITTING TIMES

M. Kupsa and Y. Lacroix

In this paper we characterize possible asymptotics for hitting times in
aperiodic ergodic dynamical systems: asymptotics are proved to be the
distribution functions of subprobability measures on the line belonging 
to the
functional class {6pt} {-3mm}(A){6mm}F={F:R\to [0,1]:\left\lbrack 
\matrixF is
increasing, null on ]-\infty, 0]; \noalignF is continuous and concave;
\noalignF(t)\le t for t\ge 0.\right.}. {6pt} Note that all possible 
asymptotics
are absolutely continuous.


http://front.math.ucdavis.edu/math.PR/0503655

---------------------------------------------------------------

3287. KREIN'S SPECTRAL THEORY AND THE PALEY-WIENER EXPANSION FOR 
FRACTIONAL  BROWNIAN MOTION

Kacha Dzhaparidze and Harry van Zanten

In this paper we develop the spectral theory of the fractional Brownian
motion (fBm) using the ideas of Krein's work on continuous analogous of
orthogonal polynomials on the unit circle. We exhibit the functions 
which are
orthogonal with respect to the spectral measure of the fBm and obtain an
explicit reproducing kernel in the frequency domain. We use these 
results to
derive an extension of the classical Paley-Wiener expansion of the 
ordinary
Brownian motion to the fractional case.


http://front.math.ucdavis.edu/math.PR/0503656

---------------------------------------------------------------

3288. CRITICALITY FOR BRANCHING PROCESSES IN RANDOM ENVIRONMENT

V. I. Afanasyev and  J. Geiger and  G. Kersting and V. A. Vatutin

We study branching processes in an i.i.d. random environment, where the
associated random walk is of the oscillating type. This class of 
processes
generalizes the classical notion of criticality. The main properties of 
such
branching processes are developed under a general assumption, known as
Spitzer's condition in fluctuation theory of random walks, and some 
additional
moment condition. We determine the exact asymptotic behavior of the 
survival
probability and prove conditional functional limit theorems for the 
generation
size process and the associated random walk. The results rely on a 
stimulating
interplay between branching process theory and fluctuation theory of 
random
walks.


http://front.math.ucdavis.edu/math.PR/0503657

---------------------------------------------------------------

3289. EXAMPLES OF MODERATE DEVIATION PRINCIPLE FOR DIFFUSION PROCESSES

A. Guillin} and  R. Liptser

Taking into account some likeness of moderate deviations (MD) and 
central
limit theorems (CLT), we develop an approach, which made a good showing 
in CLT,
for MD analysis of a family $$ 
S^\kappa_t=\frac{1}{t^\kappa}\int_0^tH(X_s)ds, \
t\to\infty $$ for an ergodic diffusion process $X_t$ under 
$0.5<\kappa<1$ and
appropriate $H$. We mean a decomposition with ``corrector'': $$
\frac{1}{t^\kappa}\int_0^tH(X_s)ds={\rm
corrector}+\frac{1}{t^\kappa}\underbrace{M_t}_{\rm martingale}. $$ and 
show
that, as in the CLT analysis, the corrector is negligible but in the MD 
scale,
and the main contribution in the MD brings the family ``$
\frac{1}{t^\kappa}M_t, t\to\infty. $'' Starting from Bayer and Freidlin,
\cite{BF}, and finishing by Wu's papers \cite{Wu1}-\cite{WuH}, in the 
MD study
Laplace's transform dominates. In the paper, we replace the Laplace 
technique
by one, admitting to give the conditions, providing the MD, in terms of
``drift-diffusion'' parameters and $H$. However, a verification of these
conditions heavily depends on a specificity of a diffusion model. That 
is why
the paper is named ``Examples ...''.


http://front.math.ucdavis.edu/math.PR/0503070

---------------------------------------------------------------

3290. CONFIDENCE INTERVALS FOR NONHOMOGENEOUS BRANCHING PROCESSES AND  
POLYMERASE CHAIN REACTIONS

Didier Piau

We extend in two directions our previous results about the sampling and 
the
empirical measures of immortal branching Markov processes. Direct 
applications
to molecular biology are rigorous estimates of the mutation rates of 
polymerase
chain reactions from uniform samples of the population after the 
reaction.
First, we consider nonhomogeneous processes, which are more adapted to 
real
reactions. Second, recalling that the first moment estimator is 
analytically
known only in the infinite population limit, we provide rigorous 
confidence
intervals for this estimator that are valid for any finite population. 
Our
bounds are explicit, nonasymptotic and valid for a wide class of 
nonhomogeneous
branching Markov processes that we describe in detail. In the setting of
polymerase chain reactions, our results imply that enlarging the size 
of the
sample becomes useless for surprisingly small sizes. Establishing 
confidence
intervals requires precise estimates of the second moment of random 
samples.
The proof of these estimates is more involved than the proofs that 
allowed us,
in a previous paper, to deal with the first moment. On the other hand, 
our
method uses various, seemingly new, monotonicity properties of the 
harmonic
moments of sums of exchangeable random variables.


http://front.math.ucdavis.edu/math.PR/0503659

---------------------------------------------------------------

3291. SECTORIAL CONVERGENCE OF U-STATISTICS

Anda Gadidov

In this note we show that almost sure convergence to zero of symmetrized
U-statistics indexed by a linear sector in Z^d_+ is equivalent to 
convergence
along the diagonal of Z^d_+, as it is considered in Lata\la and Zinn 
[Ann.
Probab. 28 (2000) 1908-1924]. Comparisons with similar results for sums 
of
multi-indexed i.i.d. random variables are also made.


http://front.math.ucdavis.edu/math.PR/0503660

---------------------------------------------------------------

3292. A STRONG INVARIANCE PRINCIPLE FOR ASSOCIATED RANDOM FIELDS

Raluca M. Balan

In this paper we generalize Yu's [Ann. Probab. 24 (1996) 2079-2097] 
strong
invariance principle for associated sequences to the multi-parameter 
case,
under the assumption that the covariance coefficient u(n) decays 
exponentially
as n\to \infty. The main tools that we use are the following: the 
Berkes and
Morrow [Z. Wahrsch. Verw. Gebiete 57 (1981) 15-37] multi-parameter 
blocking
technique, the Csorgo and Revesz [Z. Wahrsch. Verw. Gebiete 31 (1975) 
255-260]
quantile transform method and the Bulinski [Theory Probab. Appl. 40 
(1995)
136-144] rate of convergence in the CLT.


http://front.math.ucdavis.edu/math.PR/0503661

---------------------------------------------------------------

3293. MODERATE DEVIATION PRINCIPLE FOR ERGODIC MARKOV CHAIN. LIPSCHITZ  
SUMMANDS

B. Delyon and  A. Juditsky and  R. Liptser

For ${1/2}<\alpha<1$, we propose the MDP analysis for family $$
S^\alpha_n=\frac{1}{n^\alpha}\sum_{i=1}^nH(X_{i-1}), n\ge 1, $$ where
$(X_n)_{n\ge 0}$ be a homogeneous ergodic Markov chain, $X_n\in 
\mathbb{R}^d$,
when the spectrum of operator $P_x$ is continuous. The vector-valued 
function
$H$ is not assumed to be bounded but the Lipschitz continuity of $H$ is
required. The main helpful tools in our approach are Poisson's equation 
and
Stochastic Exponential; the first enables to replace the original 
family by
$\frac{1}{n^\alpha}M_n$ with a martingale $M_n$ while the second to 
avoid the
direct Laplace transform analysis.


http://front.math.ucdavis.edu/math.PR/0503071

---------------------------------------------------------------

3294. DISTANCES IN RANDOM GRAPHS WITH FINITE MEAN AND INFINITE VARIANCE 
  DEGREES

Remco van der Hofstad and  Gerard Hooghiemstra and  Dmitri Znamenski

In this paper we study random graphs with independent and identically
distributed degrees of which the tail of the distribution function is 
regularly
varying with exponent $\tau\in (2,3)$.
   The number of edges between two arbitrary nodes, also called the graph
distance or hopcount, in a graph with $N$ nodes is investigated when 
$N\to
\infty$. When $\tau\in (2,3)$, this graph distance grows like 
$2\frac{\log\log
N}{|\log(\tau-2)|}$. In different papers, the cases $\tau>3$ and 
$\tau\in
(1,2)$ have been studied. We also study the fluctuations around these
asymptotic means, and describe their distributions. The results 
presented here
improve upon results of Reittu and Norros, who prove an upper bound 
only.


http://front.math.ucdavis.edu/math.PR/0502581

---------------------------------------------------------------

3295. ON TAIL DISTRIBUTIONS OF SUPREMUM AND QUADRATIC VARIATION OF 
LOCAL  MARTINGALES

R. Liptser and  A. Novikov

We extend some known results relating the distribution tails of a 
continuous
local martingale supremum and its quadratic variation to the case of 
locally
square integrable martingales with bounded jumps. The predictable and 
optional
quadratic variations are involved in the main result.


http://front.math.ucdavis.edu/math.PR/0503072

---------------------------------------------------------------

3296. LIMIT THEOREMS FOR BIPOWER VARIATION IN FINANCIAL ECONOMETRICS

Ole E. Barndorff-Nielsen (DEPT Math Sci) and  Svend E. Graversen (DEPT  
Math Sci), Jean Jacod (PMA), Neil Shephard (NUFFIELD College)

In this paper we provide an asymptotic analysis of generalised bipower
measures of the variation of price processes in financial economics. 
These
measures encompass the usual quadratic variation, power variation and 
bipower
variations which have been highlighted in recent years in financial
econometrics. The analysis is carried out under some rather general 
Brownian
semimartingale assumptions, which allow for standard leverage effects.


http://front.math.ucdavis.edu/math.PR/0503711

---------------------------------------------------------------

3297. RANDOM WALKS IN A DIRICHLET ENVIRONMENT

Nathana\"el Enriquez and  Christophe Sabot

This paper states a law of large numbers for a random walk in a random 
iid
environment on ${\mathbb Z}^d$, where the environment follows some 
Dirichlet
distribution. Moreover, we give explicit bounds for the asymptotic 
velocity of
the process and also an asymptotic expansion of this velocity at low 
disorder.


http://front.math.ucdavis.edu/math.PR/0503713

---------------------------------------------------------------

3298. RANDOM WALKS IN A RANDOM ENVIRONMENT

S R S Varadhan

Random walks as well as diffusions in random media are considered. 
Methods
are developed that allow one to establish large deviation results for 
both the
`quenched' and the `averaged' case.


http://front.math.ucdavis.edu/math.PR/0503089

---------------------------------------------------------------

3299. RANDOM TREES AND GENERAL BRANCHING PROCESSES

Anna Rudas and  Balint Toth and  Benedek Valko

We consider a model of random tree growth, where at each time unit a new
vertex is added and attached to an already existing vertex chosen at 
random.
The probability with which a vertex with degree $k$ is chosen is 
proportional
to $w(k)$, where the weight function $w$ is the parameter of the model.
   In the papers of B. Bollobas, O. Riordan, J. Spencer, G. Tusnady, and,
independently, Mori, the asymptotic degree distribution is obtained for 
a model
that is equivalent to the special case of ours, when the weight 
function is
linear. The proof therein strongly relies on the linear choice of $w$.
   We give the asymptotical degree distribution for a wide range of 
weight
functions. Moreover, we provide the asymptotic distribution of the tree 
itself
as seen from a randomly selected vertex. The latter approach is new and 
gives
full insight to the limiting structure of the tree.
   Our proof relies on the fact that considering the evolution of the 
random
tree in continuous time, the process may be viewed as a general 
branching
process, this way classical results can be applied.


http://front.math.ucdavis.edu/math.PR/0503728

---------------------------------------------------------------

3300. MIXED POISSON APPROXIMATION OF NODE DEPTH DISTRIBUTIONS IN RANDOM 
BINARY  SEARCH TREES

Rudolf Grubel and Nikolce Stefanoski

We investigate the distribution of the depth of a node containing a 
specific
key or, equivalently, the number of steps needed to retrieve an item 
stored in
a randomly grown binary search tree. Using a representation in terms of 
mixed
and compounded standard distributions, we derive approximations by 
Poisson and
mixed Poisson distributions; these lead to asymptotic normality 
results. We are
particularly interested in the influence of the key value on the 
distribution
of the node depth. Methodologically our message is that the explicit
representation may provide additional insight if compared to the 
standard
approach that is based on the recursive structure of the trees. 
Further, in
order to exhibit the influence of the key on the distributional 
asymptotics, a
suitable choice of distance of probability distributions is important. 
Our
results are also applicable in connection with the number of recursions 
needed
in Hoare's [Comm. ACM 4 (1961) 321-322] selection algorithm Find.


http://front.math.ucdavis.edu/math.PR/0503738

---------------------------------------------------------------

3301. ON FRACTIONAL TEMPERED STABLE MOTION

C. Houdr\'e and  R. Kawai

Fractional tempered stable motion (fTSm)} is defined and studied. FTSm 
has
the same covariance structure as fractional Brownian motion, while 
having tails
heavier than Gaussian but lighter than stable. Moreover, in short time 
it is
close to fractional stable L\'evy motion, while it is approximately 
fractional
Brownian motion in long time. A series representation of fTSm is 
derived and
used for simulation and to study some of its sample path properties.


http://front.math.ucdavis.edu/math.PR/0503741

---------------------------------------------------------------

3302. ON LAYERED STABLE PROCESSES

C. Houdr\'e and  R. Kawai

Layered stable (multivariate) distributions and processes are defined 
and
studied. A layered stable process combines stable trends of two 
different
indices, one of them possibly Gaussian. More precisely, in short time, 
it is
close to a stable process while, in long time, it approximates another 
stable
(possibly Gaussian) process. We also investigate the absolute 
continuity of a
layered stable process with respect to its short time limiting stable 
process.
A series representation of layered stable processes is derived, giving 
insights
into both the structure of the sample paths and of the short and long 
time
behaviors. This series is further used for sample paths simulation.


http://front.math.ucdavis.edu/math.PR/0503742

---------------------------------------------------------------

3303. MEASURE FREE MARTINGALES

Rajeeva L Karandikar and M G Nadkarni

We give a necessary and sufficient condition on a sequence of functions 
on a
set $\Omega$ under which there is a measure on $\Omega$ which renders 
the given
sequence of functions a martingale. Further such a measure is unique if 
we
impose a natural maximum entropy condition on the conditional 
probabilities.


http://front.math.ucdavis.edu/math.PR/0503099

---------------------------------------------------------------

3304. METRIC STABILITY FOR RANDOM WALKS (WITH APPLICATIONS IN 
RENORMALIZATION  THEORY)

Carlos G. Moreira (IMPA-Brazil) Daniel Smania (ICMC-USP-Brazil)

Consider deterministic random walks F: I x Z -> I x Z, defined by
F(x,n)=(f(x), K(x)+n), where f is an expanding Markov map on the 
interval I and
K: I->Z. We study the universality (stability) of ergodic (for instance,
recurrence and transience), geometric and multifractal properties in 
the class
of perturbations of the type G(x,n)=(f_n(x), L(x,n)+n) which are 
topologically
conjugate with F and f_n are expanding maps exponentially close to f 
when |n|
goes to infinity. We give applications of these results in the study of 
the
regularity of conjugacies between (generalized) infinitely 
renormalizable maps
of the interval and the existence of wild attractors for 
one-dimensional maps.


http://front.math.ucdavis.edu/math.DS/0503736

---------------------------------------------------------------

3305. THE JAMMED PHASE OF THE BIHAM-MIDDLETON-LEVINE TRAFFIC MODEL

Omer Angel and  Alexander E Holroyd and James B Martin

Initially a car is placed with probability p at each site of the
two-dimensional integer lattice. Each car is equally likely to be 
East-facing
or North-facing, and different sites receive independent assignments. 
At odd
time steps, each North-facing car moves one unit North if there is a 
vacant
site for it to move into. At even time steps, East-facing cars move 
East in the
same way. We prove that when p is sufficiently close to 1 traffic is 
jammed, in
the sense that no car moves infinitely many times. The result extends to
several variant settings, including a model with cars moving at random 
times,
and higher dimensions.


http://front.math.ucdavis.edu/math.PR/0504001

---------------------------------------------------------------

3306. BSDE WITH QUADRATIC GROWTH AND UNBOUNDED TERMINAL VALUE

Philippe Briand (IRMAR) and  Ying Hu (IRMAR)

In this paper, we study the existence of solution to BSDE with quadratic
growth and unbounded terminal value. We apply a localization procedure 
together
with a priori bounds. As a byproduct, we apply the same method to 
extend a
result on BSDEs with integrable terminal condition.


http://front.math.ucdavis.edu/math.PR/0504002

---------------------------------------------------------------

3307. THE HEAT EQUATION WITH MULTIPLICATIVE STABLE L\'EVY NOISE

Carl Mueller and Leonid Mytnik and Aurel Stan

We study the heat equation with a random potential term. The potential 
is a
one-sided stable noise, with positive jumps, which does not depend on 
time. To
avoid singularities, we define the equation in terms of a construction 
similar
to the Skorokhod integral or Wick product. We give a criterion for 
existence
based on the dimension of the space variable, and the parameter p of 
the stable
noise. Our arguments are different for p<1 and p>1.


http://front.math.ucdavis.edu/math.PR/0504027

---------------------------------------------------------------

3308. THE FULL SCALING LIMIT OF TWO-DIMENSIONAL CRITICAL PERCOLATION

Federico Camia and  Charles M. Newman

We use SLE(6) paths to construct a process of continuum nonsimple loops 
in
the plane and prove that this process coincides with the full continuum 
scaling
limit of 2D critical site percolation on the triangular lattice -- that 
is, the
scaling limit of the set of all interfaces between different clusters. 
Some
properties of the loop process, including conformal invariance, are also
proved. In the main body of the paper these results are proved while 
assuming,
as argued by Schramm and Smirnov, that the percolation exploration path
converges in distribution to the trace of chordal SLE(6). Then, in a 
lengthy
appendix, a detailed proof is provided for this convergence to SLE(6), 
which
itself relies on Smirnov's result that crossing probabilities converge 
to
Cardy's formula.


http://front.math.ucdavis.edu/math.PR/0504036

---------------------------------------------------------------

3309. MINIMAX AND ADAPTIVE ESTIMATION OF THE WIGNER FUNCTION IN QUANTUM 
  HOMODYNE TOMOGRAPHY WITH NOISY DATA

Cristina Butucea (PMA and  MODALX) and  Madalin Guta and  Luis Artiles

We estimate the quantum state of a light beam from results of quantum
homodyne measurements performed on identically prepared quantum 
systems. The
state is represented through the Wigner function, a density on R2 which 
may
take negative values but must respect intrinsic positivity constraints 
imposed
by quantum physics. The effect of the losses due to detection 
inefficiencies
which are always present in a real experiment is the addition to the
tomographic data of independent Gaussian noise. We construct a kernel 
estimator
for the Wigner function and prove that it is minimax efficient for the
pointwise risk over a class of infinitely differentiable functions. For 
the L2
risk, we compute the upper bounds of a truncated kernel estimator over 
the same
classes, restricted to functions with sub-Gaussian asymptotic 
behaviour. We
construct adaptive estimators, i.e. which do not depend on the 
smoothness
parameters, and prove that in some set-ups they attain the minimax 
rates for
the corresponding smoothness class.


http://front.math.ucdavis.edu/math.PR/0504058

---------------------------------------------------------------

3310. POINT PROCESS MODEL OF 1/F NOISE VERSUS A SUM OF LORENTZIANS

B. Kaulakys and  V. Gontis and  and M. Alaburda

We present a simple point process model of $1/f^{\beta}$ noise, covering
different values of the exponent $\beta$. The signal of the model 
consists of
pulses or events. The interpulse, interevent, interarrival, recurrence 
or
waiting times of the signal are described by the general Langevin 
equation with
the multiplicative noise and stochastically diffuse in some interval 
resulting
in the power-law distribution. Our model is free from the requirement 
of a wide
distribution of relaxation times and from the power-law forms of the 
pulses. It
contains only one relaxation rate and yields $1/f^ {\beta}$ spectra in 
a wide
range of frequency. We obtain explicit expressions for the power 
spectra and
present numerical illustrations of the model. Further we analyze the 
relation
of the point process model of $1/f$ noise with the 
Bernamont-Surdin-McWhorter
model, representing the signals as a sum of the uncorrelated 
components. We
show that the point process model is complementary to the model based 
on the
sum of signals with a wide-range distribution of the relaxation times. 
In
contrast to the Gaussian distribution of the signal intensity of the 
sum of the
uncorrelated components, the point process exhibits asymptotically a 
power-law
distribution of the signal intensity. The developed multiplicative point
process model of $1/f^{\beta}$ noise may be used for modeling and 
analysis of
stochastic processes in different systems with the power-law 
distribution of
the intensity of pulsing signals.


http://front.math.ucdavis.edu/cond-mat/0504025

---------------------------------------------------------------

3311. A RANDOM WALK PROOF OF THE ERDOS-TAYLOR CONJECTURE

Jay Rosen

For the simple random walk in Z^2 we study those points which are 
visited an
unusually large number of times, and provide a new proof of the 
Erdos-Taylor
conjecture describing the number of visits to the most visited point.


http://front.math.ucdavis.edu/math.PR/0503108

---------------------------------------------------------------

3312. WHAT IS ALWAYS STABLE IN NONLINEAR FILTERING?

P. Chigansky and  R. Liptser

This note addresses certain stability properties of the nonlinear 
filtering
equation in discrete time. The available positive and negative results 
indicate
that much depends on the structure of the signal state space, its 
ergodic
properties and observations regularity. We show that certain predicting
estimates are stable under surprisingly general assumptions.


http://front.math.ucdavis.edu/math.PR/0504094

---------------------------------------------------------------

3313. HOW LIKELY IS AN I.I.D. DEGREE SEQUENCE TO BE GRAPHICAL?

Richard Arratia and Thomas M. Liggett

Given i.i.d. positive integer valued random variables D_1,...,D_n, one 
can
ask whether there is a simple graph on n vertices so that the degrees 
of the
vertices are D_1,...,D_n. We give sufficient conditions on the 
distribution of
D_i for the probability that this be the case to be asymptotically 0, 
{1/2} or
strictly between 0 and {1/2}. These conditions roughly correspond to 
whether
the limit of nP(D_i\geq n) is infinite, zero or strictly positive and 
finite.
This paper is motivated by the problem of modeling large communications
networks by random graphs.


http://front.math.ucdavis.edu/math.PR/0504096

---------------------------------------------------------------

3314. THE UNIVERSALITY CLASSES IN THE PARABOLIC ANDERSON MODEL

Remco van der Hofstad and  Wolfgang Koenig and  Peter Moerters

We discuss the long time behaviour of the parabolic Anderson model, the
Cauchy problem for the heat equation with random potential on $\Z^d$. We
consider general i.i.d. potentials and show that exactly \emph{four}
qualitatively different types of intermittent behaviour can occur. 
These four
universality classes depend on the upper tail of the potential 
distribution:
(1) tails at $\infty$ that are thicker than the double-exponential 
tails, (2)
double-exponential tails at $\infty$ studied by G\"artner and 
Molchanov, (3) a
new class called \emph{almost bounded potentials}, and (4) potentials 
bounded
from above studied by Biskup and K\"onig. The new class (3), which 
contains
both unbounded and bounded potentials, is studied in both the annealed 
and the
quenched setting. We show that intermittency occurs on unboundedly 
increasing
islands whose diameter is slowly varying in time. The characteristic
variational formulas describing the optimal profiles of the potential 
and of
the solution are solved explicitly by parabolas, respectively, Gaussian
densities.


http://front.math.ucdavis.edu/math.PR/0504102

---------------------------------------------------------------

3315. INVARIANCE PRINCIPLES FOR LABELED MOBILES AND BIPARTITE PLANAR 
MAPS

Jean-Fran\c{c}ois Marckert (LM-Versailles) and  Gr\'{e}gory Miermont  
(LM-Orsay)

A class of labeled trees, called mobiles, was introduced by Bouttier-di
Francesco and Guitter in order to generalize the bijective studies of 
planar
maps initiated by Cori-Vauquelin and Schaeffer. We prove an invariance
principle for rescaled random mobiles associated with bipartite random 
planar
maps under a Boltzmann distribution. We infer that the latter converge 
in a
certain sense to the Brownian map introduced by Marckert and Mokkadem, 
which
encompasses results of Chassaing and Schaeffer on quadrangulations 
(although in
a slightly different context). These results are derived from a new 
invariance
principle for a class of two-type Galton-Watson trees coupled with a 
spatial
motion, which are shown to converge to the Brownian snake.


http://front.math.ucdavis.edu/math.PR/0504110

---------------------------------------------------------------

3316. TRACY-WIDOM LIMIT FOR THE LARGEST EIGENVALUE OF A LARGE CLASS OF 
COMPLEX  WISHART MATRICES

Noureddine El Karoui

We study the limiting behavior of the largest eigenvalue of a large 
class of
complex Wishart matrices. In other words, let X be an n*p matrix, and 
let its
rows be i.i.d complex normal N_{C}(0,Sigma_p). We denote by H_p the 
spectral
distribution of Sigma_p, and call lambda_i's its ordered eigenvalues. 
Let us
call l_i's the ordered eigenvalues of X^*X and c the unique root in
[0,1/lambda_1(Sigma_p)) of the equation
   \int ((lambda c)/(1-\lambda c))^2 dH_p(lambda) = n/p. The main result 
of this
paper is that, under technical conditions on (Sigma_p,n,p), we have, 
when
n->\infty,
   (l_1(X^*X)-n mu)/(n^{1/3} sigma) -> TW_2 .
  We give explicit formulas for mu and sigma, that depend non trivially 
on c.
Here TW_2 denotes the Tracy-Widom law appearing in the study of the 
Gaussian
Unitary Ensemble.
   This theorem applies to a number of covariance models found in 
applications,
including well-behaved Toeplitz matrices and covariance matrices whose 
spectral
distribution is a sum of atoms (under some conditions on the mass of the
atoms). Generalizations of the theorem to certain spiked versions of 
models in
G and a.s statements about l_1/n are given. Most known examples of 
convergence
of the largest eigenvalue of a complex sample covariance matrix to this
Tracy-Widom law are subcases of this result.


http://front.math.ucdavis.edu/math.PR/0503109

---------------------------------------------------------------

3317. DETERMINANTAL PROCESSES AND INDEPENDENCE

J. Ben Hough and  Manjunath Krishnapur and  Yuval Peres and Balint Virag

We give a probabilistic introduction to determinantal and permanental 
point
processes. Determinantal processes arise in physics (fermions, 
eigenvalues of
random matrices) and in combinatorics (nonintersecting paths, random 
spanning
trees). They have the striking property that the number of points in a 
region
$D$ is a sum of independent Bernoulli random variables, with parameters 
which
are eigenvalues of the relevant operator on $L^2(D)$. Moreover, any
determinantal process can be represented as a mixture of determinantal
projection processes. We give a simple explanation for these known 
facts, and
establish analogous representations for permanental processes, with 
geometric
variables replacing the Bernoulli variables. These representations lead 
to
simple proofs of existence criteria and central limit theorems, and 
unify known
results on the distribution of absolute values in certain processes with
radially symmetric distributions.


http://front.math.ucdavis.edu/math.PR/0503110

---------------------------------------------------------------

3318. RANDOM WALK ON THE INCIPIENT INFINITE CLUSTER ON TREES

Martin T. Barlow and Takashi Kumagai

Let ${\cal G}$ be the incipient infinite cluster (IIC) for percolation 
on a
homogeneous tree of degree $n_0+1$. We obtain estimates for the 
transition
density of the continuous time simple random walk $Y$ on ${\cal G}$; the
process satisfies anomalous diffusion and has spectral dimension 4/3.


http://front.math.ucdavis.edu/math.PR/0503118

---------------------------------------------------------------

3319. QUANTITATIVE CONCENTRATION INEQUALITIES FOR EMPIRICAL MEASURES ON 
  NON-COMPACT SPACES

Francois Bolley and  Arnaud Guillin and  Cedric Villani

We establish some quantitative concentration estimates for the empirical
measure of many independent variables, in transportation distances. As 
an
application, we provide some error bounds for particle simulations in a 
model
mean field problem. The tools include coupling arguments, as well as 
regularity
and moments estimates for solutions of certain diffusive partial 
differential
equations.


http://front.math.ucdavis.edu/math.PR/0503123

---------------------------------------------------------------

3320. ON THE BIAS OF TRACEROUTE SAMPLING; OR, POWER-LAW DEGREE 
DISTRIBUTIONS  IN REGULAR GRAPHS

Dimitris Achlioptas and  Aaron Clauset and  David Kempe and  and 
Cristopher Moore

Understanding the structure of the Internet graph is a crucial step for
building accurate network models and designing efficient algorithms for
Internet applications. Yet, obtaining its graph structure is a 
surprisingly
difficult task, as edges cannot be explicitly queried. Instead, 
empirical
studies rely on traceroutes to build what are essentially single-source,
all-destinations, shortest-path trees. These trees only sample a 
fraction of
the network's edges, and a recent paper by Lakhina et al. found 
empirically
that the resuting sample is intrinsically biased. For instance, the 
observed
degree distribution under traceroute sampling exhibits a power law even 
when
the underlying degree distribution is Poisson.
   In this paper, we study the bias of traceroute sampling 
systematically, and,
for a very general class of underlying degree distributions, calculate 
the
likely observed distributions explicitly. To do this, we use a 
continuous-time
realization of the process of exposing the BFS tree of a random graph 
with a
given degree distribution, calculate the expected degree distribution 
of the
tree, and show that it is sharply concentrated. As example applications 
of our
machinery, we show how traceroute sampling finds power-law degree 
distributions
in both delta-regular and Poisson-distributed random graphs. Thus, our 
work
puts the observations of Lakhina et al. on a rigorous footing, and 
extends them
to nearly arbitrary degree distributions.


http://front.math.ucdavis.edu/cond-mat/0503087

---------------------------------------------------------------

3321. THE CRITICAL ISING MODEL ON TREES, CONCAVE RECURSIONS AND 
NONLINEAR  CAPACITY

Robin Pemantle and Yuval Peres

We consider the Ising model on a general tree under various boundary
conditions: all plus, free and spin-glass. In each case, we determine 
when the
root is influenced by the boundary values in the limit as the boundary 
recedes
to infinity. We obtain exact capacity criteria that govern behavior at 
critical
temperatures. For plus boundary conditions, an $L^3$ capacity arises. In
particular, on a spherically symmetric tree that has $n^c b^n$ vertices 
at
level $n$ (up to bounded factors), we prove that there is a unique Gibbs
measure for the ferromagnetic Ising model if and only if $c$ is at most 
1/2.
Our proofs are based on a new link between nonlinear recursions on 
trees and
$L^p$ capacities.


http://front.math.ucdavis.edu/math.PR/0503137

---------------------------------------------------------------

3322. HOW LARGE A DISC IS COVERED BY A RANDOM WALK IN $N$ STEPS?

Amir Dembo and  Yuval Peres and Jay Rosen

We show that the largest disc covered by a simple random walk on the 
planar
square lattice after $n$ steps has radius $n^{1/4+o(1)}$, thus 
resolving an
open problem of P. R\'ev\'esz (1990). We also show that almost surely, 
for
infinitely many values of $n$ it takes about $n^{1/2+o(1)}$ steps after 
step
$n$ for the random walk to reach the first previously unvisited site 
(and the
exponent 1/2 is sharp). This resolves a problem raised by P. R\'ev\'esz 
(1993).
Additional results on multiple covering are obtained as well.


http://front.math.ucdavis.edu/math.PR/0503139

---------------------------------------------------------------

3323. INFINITE DIMENSIONAL STOCHASTIC DIFFERENTIAL EQUATIONS OF  
ORNSTEIN-UHLENBECK TYPE

Siva R. Athreya and  Richard F. Bass and  Maria Gordina and  Edwin A. 
Perkins

We consider the operator $$\sL f(x)=\tfrac12 \sum_{i,j=1}^\infty
a_{ij}(x)\frac{\del^2 f}{\del x_i \del x_j}(x)-\sum_{i=1}^\infty \lam_i 
x_i
b_i(x) \frac{\del f}{\del x_i}(x).$$ We prove existence and uniqueness 
of
solutions to the martingale problem for this operator under appropriate
conditions on the $a_{ij}, b_i$, and $\lam_i$. The process 
corresponding to
$\sL$ solves an infinite dimensional stochastic differential equation 
similar
to that for the infinite dimensional Ornstein-Uhlenbeck process.


http://front.math.ucdavis.edu/math.PR/0503165

---------------------------------------------------------------

3324. ON CHORDAL AND BILATERAL SLE IN MULTIPLY CONNECTED DOMAINS

Robert O. Bauer and  Roland M. Friedrich

We discuss the possible candidates for conformally invariant random
non-self-crossing curves which begin and end on the boundary of a 
multiply
connected planar domain, and which satisfy a Markovian-type property. We
consider both, the case when the curve connects a boundary component to 
itself
(chordal), and the case when the curve connects two different boundary
components (bilateral). We establish appropriate extensions of Loewner's
equation to multiply connected domains for the two cases. We show that 
a curve
in the domain induces a motion on the boundary and that this motion is 
enough
to first recover the motion of the moduli of the domain and then, 
second, the
curve in the interior. For random curves in the interior we show that 
the
induced random motion on the boundary is not Markov if the domain is 
multiply
connected, but that the random motion on the boundary together with the 
random
motion of the moduli forms a Markov process. In the chordal case, we 
show that
this Markov process satisfies Brownian scaling and discuss how this 
limits the
possible conformally invariant random non-self-crossing curves. We show 
that
the possible candidates are labeled by a real constant and a function
homogeneous of degree minus one which describes the interaction of the 
random
curve with the boundary. We show that the random curve has the locality
property if the interaction term vanishes and the real parameter equals 
six.


http://front.math.ucdavis.edu/math.PR/0503178

---------------------------------------------------------------

3325. FROM N-PARAMETER FRACTIONAL BROWNIAN MOTIONS TO N-PARAMETER  
MULTIFRACTIONAL BROWNIAN MOTIONS

E. Herbin

Multifractional Brownian motion is an extension of the well-known 
fractional
Brownian motion where the Holder regularity is allowed to vary along 
the paths.
In this paper, two kind of multi-parameter extensions of mBm are 
studied: one
is isotropic while the other is not. For each of these processes, a 
moving
average representation, a harmonizable representation, and the 
covariance
structure are given. The Holder regularity is then studied. In 
particular, the
case of an irregular exponent function H is investigated. In this 
situation,
the almost sure pointwise and local Holder exponents of the 
multi-parameter mBm
are proved to be equal to the correspondent exponents of H. Eventually, 
a local
asymptotic self-similarity property is proved. The limit process can be 
another
process than fBm.


http://front.math.ucdavis.edu/math.PR/0503182

---------------------------------------------------------------

3326. EXAMPLES OF GROUPS THAT ARE MEASURE EQUIVALENT TO THE FREE GROUP

Damien Gaboriau (UMPA-ENSL)

Measure Equivalence (ME) is the measure theoretic counterpart of
quasi-isometry. This field grew considerably during the last years, 
developing
tools to distinguish between different ME classes of countable groups. 
On the
other hand, contructions of ME equivalent groups are very rare. We 
present a
new method, based on a notion of measurable free-factor, and we apply 
it to
exhibit a new family of groups that are measure equivalent to the free 
group.
We also present a quite extensive survey on results about Measure 
Equivalence
for countable groups.


http://front.math.ucdavis.edu/math.DS/0503181

---------------------------------------------------------------

3327. ORTHOGONAL POLYNOMIALS AND FLUCTUATIONS OF RANDOM MATRICES

Timothy Kusalik and  James A. Mingo and  and Roland Speicher

In this paper we establish a connection between the fluctuations of 
Wishart
random matrices, shifted Chebyshev polynomials, and planar diagrams 
whose
linear span form a basis for the irreducible representations of the 
annular
Temperly-Lieb algebra.


http://front.math.ucdavis.edu/math.OA/0503169

---------------------------------------------------------------

3328. COUNTING CONNECTED GRAPHS ASYMPTOTICALLY

Remco van der Hofstad and  Joel Spencer

We find the asymptotic number of connected graphs with $k$ vertices and
$k-1+l$ edges when $k,l$ approach infinity, reproving a result of 
Bender,
Canfield and McKay. We use the {\em probabilistic method}, analyzing
breadth-first search on the random graph $G(k,p)$ for an appropriate 
edge
probability $p$. Central is analysis of a random walk with fixed 
beginning and
end which is tilted to the left.


http://front.math.ucdavis.edu/math.CO/0502579

---------------------------------------------------------------

3329. ON Q-FUNCTIONAL EQUATIONS AND EXCURSION MOMENTS

Christoph Richard

We analyse q-functional equations arising from tree-like combinatorial
structures, which are counted by size, internal path length and certain
generalisations thereof. The corresponding counting parameters are 
labelled by
an integer k>1. We show the existence of a joint limit distribution for 
these
parameters in the limit of infinite size, if the size generating 
function has a
square root as dominant singularity. The limit distribution coincides 
with that
of integrals of (k-1)th powers of the standard Brownian excursion. Our 
method
yields a recursion for the moments of the joint distribution and admits 
an
extension to other types of singularities.


http://front.math.ucdavis.edu/math.CO/0503198

---------------------------------------------------------------

3330. A SET-INDEXED FRACTIONAL BROWNIAN MOTION

E. Herbin and E. Merzbach

We define and prove the existence of a fractional Brownian motion 
indexed by
a collection of closed subsets of a measure space. This process is a
generalization of the set-indexed Brownian motion, when the condition of
independance is relaxed. Relations with the Levy fractional Brownian 
motion and
with the fractional Brownian sheet are studied. We prove stationarity 
of the
increments and a property of self-similarity with respect to the action 
of
solid motions. Regularity conditions are exhibited. Finally, behavior 
of the
set-indexed fractional Brownian motion along increasing paths is 
analysed.


http://front.math.ucdavis.edu/math.PR/0503211

---------------------------------------------------------------

3331. ENTROPY-DRIVEN PHASE TRANSITION IN A POLYDISPERSE HARD-RODS 
LATTICE  SYSTEM

Dmitry Ioffe and  Yvan Velenik (LMRS) and  Milos Zahradnik

We study a system of rods on the 2d square lattice, with hard-core 
exclusion.
Each rod has a length between 2 and N. We show that, when N is 
sufficiently
large, and for suitable fugacity, there are several distinct Gibbs 
states, with
orientational long-range order. This is in sharp contrast with the case 
N=2
(the monomer-dimer model), for which Heilmann and Lieb proved absence 
of phase
transition at any fugacity. This is the first example of a pure 
hard-core
system with phases displaying orientational order, but not 
translational order;
this is a fundamental characteristic feature of liquid crystals.


http://front.math.ucdavis.edu/math.PR/0503222

---------------------------------------------------------------

3332. AN INDUCTIVE PROOF OF THE BERRY-ESSEEN THEOREM FOR CHARACTER 
RATIOS

Jason Fulman

Bolthausen used a variation of Stein's method to give an inductive 
proof of
the Berry-Esseen theorem for sums of independent, identically 
distributed
random variables. We modify this technique to prove a Berry-Esseen 
theorem for
character ratios of a random representation of the symmetric group on
transpositions. An analogous result is proved for Jack measure on 
partitions.


http://front.math.ucdavis.edu/math.CO/0503227

---------------------------------------------------------------

3333. MAX-SEMI-SELFDECOMPOSABLE LAWS AND RELATED PROCESSES

S Satheesh and E Sandhya

Methods of construction of Max-semi-selfdecompsable laws are given.
Implications of this method in random time changed extremal processes 
are
discussed. Max-autoregressive model is introduced and characterized 
using the
max-semi-selfdecompsable laws and exponential max-semi-stable laws. Some
comments regarding the infinite divisibility of semi-stable and 
max-semi-stable
laws are given.


http://front.math.ucdavis.edu/math.PR/0503232

---------------------------------------------------------------

3334. DISCRETE INTERPOLATION BETWEEN MONOTONE PROBABILITY AND FREE 
PROBABILITY

Romuald Lenczewski and  Rafal Salapata

We construct a sequence of states called m-monotone product states 
which give
a discrete interpolation between the monotone product of states of 
Muraki and
the free product of states of Avitzour and Voiculescu in free 
probability. We
derive the associated basic limit theorems and develop the 
combinatorics based
on non-crossing ordered partitions with monotone order starting from 
depth m.
The Hilbert space representations of the limit mixed moments in the 
invariance
principle lead to m-monotone Gaussian operators living in m-monotone 
Fock
spaces, which are truncations of the free Fock space over the 
square-integrable
functions on the non-negative real line (m=1 gives the monotone Fock 
space). A
new type of combinatorics of inner blocks leads to explicit formulas 
for the
mixed moments of m-monotone Gaussian operators, which are new even in 
the case
of monotone independent Gaussian operators with arcsine distributions.


http://front.math.ucdavis.edu/math.QA/0502570

---------------------------------------------------------------

3335. RIFFLE SHUFFLES OF DECKS WITH REPEATED CARDS

Mark Conger and D. Viswanath

By a well-known result of Bayer and Diaconis, the maximum entropy model 
of
the common riffle shuffle implies that the number of riffle shuffles 
necessary
to mix a standard deck of 52 cards is either 7 or 11 -- with the former 
number
applying when the metric used to define mixing is the total variation 
distance
and the later when it is the separation distance. This and other related
results assume all 52 cards in the deck to be distinct and require all 
$52!$
permutations of the deck to be almost equally likely for the deck to be
considered well mixed. In many instances, not all cards in the deck are
distinct and only the sets of cards dealt out to players, and not the 
order in
which they are dealt out to each player, needs to be random. We derive
transition probabilities under riffle shuffles between decks with 
repeated
cards to cover some instances of the type just described. We focus on 
decks
with cards all of which are labeled either 1 or 2 and describe the 
consequences
of having a symmetric starting deck of the form $1,...,1,2...,2$ or 
$1,2,...,
1,2$. Finally, we consider mixing times for common card games.


http://front.math.ucdavis.edu/math.PR/0503233

---------------------------------------------------------------

3336. BERMUDAN OPTION PRICING BASED ON PIECEWISE HARMONIC INTERPOLATION 
AND  THE R\'EDUITE

Frederik S. Herzberg

We consider an iterative Bermudan option pricing algorithm based on 
piecewise
harmonic interpolation and give an explicit constructive 
characterisation of
the smallest fixed point of the iteration step as the approximate price 
of the
perpetual Bermudan option. The same arguments work for a related 
iterative
algorithm based on the approximation of subharmonic functions via the 
r\'eduite
associated with a given closed $F_{\sigma}$ subset of $\RR^d$.


http://front.math.ucdavis.edu/math.PR/0503234

---------------------------------------------------------------

3337. A BRIEF NOTE ON THE SOUNDNESS OF BERMUDAN OPTION PRICING VIA 
CUBATURE

Frederik S. Herzberg

The subject of this study is an iterative Bermudan option pricing 
algorithm
based on (high-dimensional) cubature. We show that the sequence of 
Bermudan
prices (as functions of the underlying assets' logarithmic start prices)
resulting from the iteration is bounded and increases monotonely to the
approximate perpetual Bermudan option price; the convergence is linear 
in the
supremum norm with the discount factor being the convergence factor.
Furthermore, we prove a characterisation of this approximated perpetual
Bermudan price as the smallest fixed point of the iteration procedure.


http://front.math.ucdavis.edu/math.PR/0503235

---------------------------------------------------------------

3338. SPHERICAL ASYMPTOTICS FOR THE ROTOR-ROUTER MODEL IN Z^D

Lionel Levine and  Yuval Peres

The rotor-router model is a deterministic analogue of random walk 
invented by
Jim Propp. It can be used to define a deterministic aggregation model 
analogous
to internal diffusion limited aggregation. We prove an isoperimetric 
inequality
for the exit time of simple random walk from a finite region in Z^d, 
and use
this to prove that the shape of the rotor-router aggregation model in 
Z^d,
suitably rescaled, converges to a Euclidean ball in R^d.


http://front.math.ucdavis.edu/math.PR/0503251

---------------------------------------------------------------

3339. SOME EXPLICIT KREIN REPRESENTATIONS OF CERTAIN SUBORDINATORS, 
INCLUDING  THE GAMMA PROCESS

Catherine Donati-Martin (PMA) and  Marc Yor (PMA)

We give a representation of the Gamma subordinator as a Krein 
functional of
Brownian motion, using the known representations for stable 
subordinators and
Esscher transforms. In particular, we have obtained Krein 
representations of
the subordinators which govern the two parameter Poisson-Dirichlet 
family of
distributions.


http://front.math.ucdavis.edu/math.PR/0503254

---------------------------------------------------------------

3340. AN INVARIANCE PRINCIPLE FOR CONDITIONED TREES

Jean-Francois Le Gall (DMA-ENS Paris)

We consider Galton-Watson trees associated with a critical offspring
distribution and conditioned to have exactly $n$ vertices. These trees 
are
embedded in the real line by affecting spatial positions to the 
vertices, in
such a way that the increments of the spatial positions along edges of 
the tree
are independent variables distributed according to a symmetric 
probability
distribution on the real line. We then condition on the event that all 
spatial
positions are nonnegative. Under suitable assumptions on the offspring
distribution and the spatial displacements, we prove that these 
conditioned
spatial trees converge as $n\to\infty$, modulo an appropriate rescaling,
towards the conditioned Brownian tree that was studied in previous work.
Applications are given to asymptotics for random quadrangulations.


http://front.math.ucdavis.edu/math.PR/0503263

---------------------------------------------------------------

3341. ON GENERALIZED COMPUTABLE UNIVERSAL PRIORS AND THEIR CONVERGENCE

Marcus Hutter

Solomonoff unified Occam's razor and Epicurus' principle of multiple
explanations to one elegant, formal, universal theory of inductive 
inference,
which initiated the field of algorithmic information theory. His 
central result
is that the posterior of the universal semimeasure M converges rapidly 
to the
true sequence generating posterior mu, if the latter is computable. 
Hence, M is
eligible as a universal predictor in case of unknown mu. The first part 
of the
paper investigates the existence and convergence of computable universal
(semi)measures for a hierarchy of computability classes: recursive, 
estimable,
enumerable, and approximable. For instance, M is known to be 
enumerable, but
not estimable, and to dominate all enumerable semimeasures. We present 
proofs
for discrete and continuous semimeasures. The second part investigates 
more
closely the types of convergence, possibly implied by universality: in
difference and in ratio, with probability 1, in mean sum, and for 
Martin-Loef
random sequences. We introduce a generalized concept of randomness for
individual sequences and use it to exhibit difficulties regarding these 
issues.
In particular, we show that convergence fails (holds) on 
generalized-random
sequences in gappy (dense) Bernoulli classes.


http://front.math.ucdavis.edu/cs.LG/0503026

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3342. THE STABLE MANIFOLD THEOREM FOR SEMILINEAR STOCHASTIC EVOLUTION  
EQUATIONS AND STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS I: THE 
STOCHASTIC
   SEMIFLOW

Salah-Eldin A Mohammed and  Tusheng Zhang and  Huaizhong Zhao

The main objective of this work is to characterize the pathwise local
structure of solutions of semilinear stochastic evolution equations 
(see's) and
stochastic partial differential equations (spde's) near stationary 
solutions.
Such characterization is realized through the long-term behavior of the
solution field near stationary points. The analysis falls in two parts 
I, II.
In Part I (this paper), we prove a general existence and compactness 
theorem
for $C^k$-cocycles of semilinear see's and spde's. Our results cover a 
large
class of semilinear see's as well as certain semilinear spde's with
non-Lipschitz terms such as stochastic reaction diffusion equations and 
the
stochastic Burgers equation with additive infinite-dimensional noise. 
In Part
II of this work ([M-Z-Z]), we establish a local stable manifold theorem 
for
non-linear see's and spde's.


http://front.math.ucdavis.edu/math.PR/0503320

---------------------------------------------------------------

3343. THE STABLE MANIFOLD THEOREM FOR SEMILINEAR STOCHASTIC EVOLUTION  
EQUATIONS AND STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS II: EXISTENCE 
OF
   STABLE AND UNSTABLE MANIFOLDS

Salah-Eldin A. Mohammed and  Tusheng Zhang and  Huaizhong Zhao

This article is a sequel to [M.Z.Z.1] aimed at completing the
characterization of the pathwise local structure of solutions of 
semilinear
stochastic evolution equations (see's) and stochastic partial 
differential
equations (spde's) near stationary solutions. Stationary solution are 
viewed as
random points in the infinite-dimensional state space, and the 
characterization
is expressed in terms of the almost sure long-time behavior of 
trajectories of
the equation in relation to the stationary solution. More specifically, 
we
establish local stable manifold theorems for semilinear see's and spde's
(Theorems 4.1-4.4). These results give smooth stable and unstable 
manifolds in
the neighborhood of a hyperbolic stationary solution of the underlying
stochastic equation. The stable and unstable manifolds are stationary, 
live in
a stationary tubular neighborhood of the stationary solution and are
asymptotically invariant under the stochastic semiflow of the see/spde. 
The
proof uses infinite-dimensional multiplicative ergodic theory 
techniques and
interpolation arguments (Theorem 2.1).


http://front.math.ucdavis.edu/math.PR/0503321

---------------------------------------------------------------

3344. BOUNDARY HARNACK PRINCIPLE FOR FRACTIONAL POWERS OF LAPLACIAN ON 
THE  SIERPINSKI CARPET

Andrzej Stos (LMP-Clermont)

We prove the Boundary Harnack Principle related to fractional powers of
Laplacian for some natural regions in the two-dimensional Sierpinski 
carpet.
This is a natual application of a probabilistic method based on the
Ikeda-Watanabe formula


http://front.math.ucdavis.edu/math.PR/0503333

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3345. A NOTE ON EXACT LIKELIHOODS OF THE CARR-WU MODELS FOR LEVERAGE 
EFFECTS  AND VOLATILITY IN FINANCIAL ECONOMICS

Lancelot F. James

Recently Carr and Wu (2004, 2005) and also Huang and Wu (2004) show 
that most
stochastic processes used in traditional option pricing models can be 
cast as
special cases of time-changed L\'evy processes. In particular these are 
models
which can be tailored to exhibit correlated jumps in both the log price 
of
assets and the instantaneous volatility. Naturally similar to a recent 
work of
Barndorff-Nielsen and Shephard (2001a, b), such models may be used in a
likelihood based framework. These likelihoods are based on the 
unobserved
integrated volatility, rather than the instantaneous volatility. James 
(2005)
establishes general results for the likelihood and estimation of a 
large class
of such models which include possible leverage effects. In this note we 
show
that exact expressions for likelihood models based on generalizations 
of Carr
and Wu (2005) and Huang and Wu (2005), follow essentially from the 
arguments in
Theorem 5.1 in James (2005) with some slight modification. This serves 
to
formally verify a claim made by James (2005).


http://front.math.ucdavis.edu/math.ST/0503314

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3346. POISSON KERNELS OF HALF-SPACES IN REAL HYPERBOLIC SPACES

T. Byczkowski and  P. Graczyk and  A. Stos

We provide an integral formula for the Poisson kernel of half-spaces for
Brownian motion in real hyperbolic space $\H^n$. This enables us to find
asymptotic properties of the kernel. Our starting point is the formula 
for its
Fourier transform. When $n=3$, 4 or 6 we give an explicit formula for 
the
Poisson kernel itself. In the general case we give various asymptotics 
and show
convergence to the Poisson kernel of $\H^n$.


http://front.math.ucdavis.edu/math.PR/0503372

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3347. DOOB'S MAXIMAL IDENTITY, MULTIPLICATIVE DECOMPOSITIONS AND 
ENLARGEMENTS  OF FILTRATIONS

A. Nikeghbali and  M. Yor

In the theory of progressive enlargements of filtrations, the 
supermartingale
$Z_{t}=\mathbf{P}(g>t\mid \mathcal{F}_{t}) $ associated with an honest 
time
$g$, and its additive (Doob-Meyer) decomposition, play an essential 
role. In
this paper, we propose an alternative approach, using a multiplicative
representation for the supermartingale $Z_{t}$, based on Doob's maximal
identity. We thus give new examples of progressive enlargements. 
Moreover, we
give, in our setting, a proof of the decomposition formula for 
martingales,
using initial enlargement techniques, and use it to obtain some path
decompositions given the maximum or minimum of some processes.


http://front.math.ucdavis.edu/math.PR/0503386

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3348. AN ANNIHILATING-BRANCHING PARTICLE MODEL FOR THE HEAT EQUATION 
WITH  AVERAGE TEMPERATURE ZERO

Krzysztof Burdzy and Jeremy Quastel

We consider two species of particles performing random walks in a 
domain in
Euclidean space with reflecting boundary conditions, which annihilate on
contact. In addition there is a conservation law so that the total 
number of
particles of each type is preserved: When the two particles of different
species annihilate each other, particles of each species, chosen at 
random,
give birth. We assume initially equal numbers of each species and show 
that the
system has a diffusive scaling limit in which the densities of the two 
species
are well approximated by the positive and negative parts of the 
solution of the
heat equation normalized to have constant $L^1$ norm. In particular, 
the higher
Neumann eigenfunctions appear as asymptotically stable states at the 
diffusive
time scale.


http://front.math.ucdavis.edu/math.PR/0503395

---------------------------------------------------------------

3349. THE REVERSIBLE NEAREST PARTICLE SYSTGEMS ON A FINITE INTERVAL

Dayue Chen and  Juxin Liu and  Fuxi Zhang

In this paper we study a one-parameter family of attractive reversible
nearest particle system on a finite interval. As the length of the 
interval
increases, the time that the nearest particle system first hits the 
empty set
increases in different order, from logarithmic to exponential, 
according to the
intensity of interaction. In particular, at the critical case, the first
hitting time increases in a polynomial order.


http://front.math.ucdavis.edu/math.PR/0503409

---------------------------------------------------------------

3350. INSIDE SINGULARITY SETS OF RANDOM GIBBS MEASURES

Julien Barral and  Stephane Seuret

We evaluate the scale at which the multifractal structure of some random
Gibbs measures becomes discernible. The value of this scale is obtained 
through
what we call the growth speed in H\"older singularity sets of a Borel 
measure.
This growth speed yields new information on the multifractal behavior 
of the
rescaled copies involved in the structure of statistically self-similar 
Gibbs
measures. Our results are useful to understand the multifractal nature 
of
various heterogeneous jump processes.


http://front.math.ucdavis.edu/math.PR/0503420

---------------------------------------------------------------

3351. RENEWAL OF SINGULARITY SETS OF STATISTICALLY SELF-SIMILAR MEASURES

Julien Barral and  Stephane Seuret

This paper investigates new properties concerning the multifractal 
structure
of a class of statistically self-similar measures. These measures 
include the
well-known Mandelbrot multiplicative cascades, sometimes called 
independent
random cascades. We evaluate the scale at which the multifractal 
structure of
these measures becomes discernible. The value of this scale is obtained 
through
what we call the growth speed in H\"older singularity sets of a Borel 
measure.
This growth speed yields new information on the multifractal behavior 
of the
rescaled copies involved in the structure of statistically self-similar
measures. Our results are useful to understand the multifractal nature 
of
various heterogeneous jump processes.


http://front.math.ucdavis.edu/math.PR/0503421

---------------------------------------------------------------

3352. A POLYHEDRAL MARKOV FIELD - PUSHING THE ARAK-SURGAILIS 
CONSTRUCTION INTO  THREE DIMENSIONS

Tomasz Schreiber

The purpose of the paper is to construct a polyhedral Markov field in
${\mathbb R}^3$ in analogy with the planar construction of the original 
Arak
(1982) polygonal Markov field. We provide a dynamic construction of the 
process
in terms of evolution of two-dimensional multi-edge systems tracing 
polyhedral
boundaries of the field in three-dimensional time-space. We also give a 
general
algorithm for simulating Gibbsian modifications of the constructed 
polyhedral
field.


http://front.math.ucdavis.edu/math.PR/0503429

---------------------------------------------------------------

3353. BAYSIAN INFERENCE VIA CLASSES OF NORMALIZED RANDOM MEASURES

Lancelot F. James and  Antonio Lijoi and Igor Pruenster

One of the main research areas in Bayesian Nonparametrics is the 
proposal and
study of priors which generalize the Dirichlet process. Here we exploit
theoretical properties of Poisson random measures in order to provide a
comprehensive Bayesian analysis of random probabilities which are 
obtained by
an appropriate normalization. Specifically we achieve explicit and 
tractable
forms of the posterior and the marginal distributions, including an 
explicit
and easily used description of generalizations of the important
Blackwell-MacQueen P\'olya urn distribution. Such simplifications are 
achieved
by the use of a latent variable which admits quite interesting 
interpretations
which allow to gain a better understanding of the behaviour of these 
random
probability measures. It is noteworthy that these models are 
generalizations of
models considered by Kingman (1975) in a non-Bayesian context. Such 
models are
known to play a significant role in a variety of applications including
genetics, physics, and work involving random mappings and assemblies. 
Hence our
analysis is of utility in those contexts as well. We also show how our 
results
may be applied to Bayesian mixture models and describe computational 
schemes
which are generalizations of known efficient methods for the case of the
Dirichlet process. We illustrate new examples of processes which can 
play the
role of priors for Bayesian nonparametric inference and finally point 
out some
interesting connections with the theory of generalized gamma 
convolutions
initiated by Thorin and further developed by Bondesson.


http://front.math.ucdavis.edu/math.ST/0503394

---------------------------------------------------------------

3354. A STOCHASTIC APPROXIMATION ALGORITHM WITH MULTIPLICATIVE STEP 
SIZE  ADAPTATION

Alexander Plakhov and  Pedro Cruz

An algorithm of searching a zero of an unknown undimensional function is
considered, measured at a point x with some error. The step sizes are 
random
positive values and are calculated according to the rule: if two 
consecutive
iterations are in same direction step is multiplied by u>1, otherwise, 
it is
multiplied by 0<d<1. The function may have one or more zeros; the 
random values
are independent and identically distributed, with zero mean and finite
variance. Under some additional assumptions on the conditions on the two
parameters u and d almost sure convergence of the sequence as well as 
under
some conditions is guaranteed almost sure divergence. In particular, if 
the
error distribuition as median 0 and zero probability for particular 
poinst then
it is established that for ud<1, convergence takes place, and for ud>1,
divergence. Due to the multiplicative rule of updating of the step, it 
is
natural to expect that the sequence converges rapidly: like a geometric
progression (if convergence takes place), but the limit value may not 
coincide
with, but instead, approximates one of zeros of the function. By 
adjusting the
parameters u and d, one can reach necessary precision of approximation; 
higher
precision is obtained at the expense of lower convergence rate.


http://front.math.ucdavis.edu/math.ST/0503434

---------------------------------------------------------------

3355. ON APPROXIMATE PATTERN MATCHING FOR A CLASS OF GIBBS RANDOM FIELDS

J.R. Chazottes and  F. Redig and  E. Verbitskiy

We prove an exponential approximation for the law of approximate 
occurrence
of typical patterns for a class of Gibbsian sources on the lattice 
$\mathbb
Z^d$, $d\ge 2$. From this result, we deduce a law of large numbers and 
a large
deviation result for the the waiting time of distorted patterns.


http://front.math.ucdavis.edu/math.PR/0503008

---------------------------------------------------------------

3356. THE BASIC REPRESENTATION OF THE CURRENT GROUP O(N,1)^X IN THE L^2 
SPACE  OVER THE GENERALIZED LEBESGUE MEASURE

A.M.Vershik and  M.I.Graev

We give the realization of the representation of the current group 
O(n,1)^X
where X is a manifold, in the Hilbert space of L^2(F,\nu) of 
functionals on the
the space F of the generalized functions on the manifold X which are 
square
integrable over measure \nu which is related to a distinguish Levy 
process with
values in R^{n-1} which generalized one dimensional gamma process. 
Unipotent
subgroup of the group O(n,1)^X acts as the group of multiplicators. 
Measure \nu
is sigma-finite and invariant under the action current group O(n-1)^X. 
Ther
case of n=2 (SL(2,R^X)) was considered before in the series of papers 
starting
from the article Vershik-Gel'fand-Graev (1973).


http://front.math.ucdavis.edu/math.RT/0503404

---------------------------------------------------------------

3357. DYNAMIC IMPORTANCE SAMPLING FOR UNIFORMLY RECURRENT MARKOV CHAINS

Paul Dupuis and Hui Wang

Importance sampling is a variance reduction technique for efficient
estimation of rare-event probabilities by Monte Carlo. In standard 
importance
sampling schemes, the system is simulated using an a priori fixed 
change of
measure suggested by a large deviation lower bound analysis. Recent 
work,
however, has suggested that such schemes do not work well in many 
situations.
In this paper we consider dynamic importance sampling in the setting of
uniformly recurrent Markov chains. By ``dynamic'' we mean that in the 
course of
a single simulation, the change of measure can depend on the outcome of 
the
simulation up till that time. Based on a control-theoretic approach to 
large
deviations, the existence of asymptotically optimal dynamic schemes is
demonstrated in great generality. The implementation of the dynamic 
schemes is
carried out with the help of a limiting Bellman equation. Numerical 
examples
are presented to contrast the dynamic and standard schemes.


http://front.math.ucdavis.edu/math.PR/0503454

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3358. THE EXIT PROBLEM FOR DIFFUSIONS WITH TIME-PERIODIC DRIFT AND 
STOCHASTIC  RESONANCE

Samuel Herrmann and Peter Imkeller

Physical notions of stochastic resonance for potential diffusions in
periodically changing double-well potentials such as the spectral power
amplification have proved to be defective. They are not robust for the 
passage
to their effective dynamics: continuous-time finite-state Markov chains
describing the rough features of transitions between different domains 
of
attraction of metastable points. In the framework of one-dimensional 
diffusions
moving in periodically changing double-well potentials we design a new 
notion
of stochastic resonance which refines Freidlin's concept of 
quasi-periodic
motion. It is based on exact exponential rates for the transition 
probabilities
between the domains of attraction which are robust with respect to the 
reduced
Markov chains. The quality of periodic tuning is measured by the 
probability
for transition during fixed time windows depending on a time scale 
parameter.
Maximizing it in this parameter produces the stochastic resonance 
points.


http://front.math.ucdavis.edu/math.PR/0503455

---------------------------------------------------------------

3359. LEARNING MIXTURES OF SEPARATED NONSPHERICAL GAUSSIANS

Sanjeev Arora and Ravi Kannan

Mixtures of Gaussian (or normal) distributions arise in a variety of
application areas. Many heuristics have been proposed for the task of 
finding
the component Gaussians given samples from the mixture, such as the EM
algorithm, a local-search heuristic from Dempster, Laird and Rubin [J. 
Roy.
Statist. Soc. Ser. B 39 (1977) 1-38]. These do not provably run in 
polynomial
time. We present the first algorithm that provably learns the component
Gaussians in time that is polynomial in the dimension. The Gaussians 
may have
arbitrary shape, but they must satisfy a ``separation condition'' which 
places
a lower bound on the distance between the centers of any two component
Gaussians. The mathematical results at the heart of our proof are 
``distance
concentration'' results--proved using isoperimetric inequalities--which
establish bounds on the probability distribution of the distance 
between a pair
of points generated according to the mixture. We also formalize the more
general problem of max-likelihood fit of a Gaussian mixture to 
unstructured
data.


http://front.math.ucdavis.edu/math.PR/0503457

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3360. FAST SIMULATION OF NEW COINS FROM OLD

Serban Nacu and Yuval Peres

Let S\subset (0,1). Given a known function f:S\to (0,1), we consider the
problem of using independent tosses of a coin with probability of heads 
p
(where p\in S is unknown) to simulate a coin with probability of heads 
f(p). We
prove that if S is a closed interval and f is real analytic on S, then 
f has a
fast simulation on S (the number of p-coin tosses needed has exponential
tails). Conversely, if a function f has a fast simulation on an open 
set, then
it is real analytic on that set.


http://front.math.ucdavis.edu/math.PR/0503458

---------------------------------------------------------------

3361. STRUCTURE OF LARGE RANDOM HYPERGRAPHS

R. W. R. Darling and J. R. Norris

The theme of this paper is the derivation of analytic formulae for 
certain
large combinatorial structures. The formulae are obtained via fluid 
limits of
pure jump-type Markov processes, established under simple conditions on 
the
Laplace transforms of their Levy kernels. Furthermore, a related 
Gaussian
approximation allows us to describe the randomness which may persist in 
the
limit when certain parameters take critical values. Our method is quite
general, but is applied here to vertex identifiability in random 
hypergraphs. A
vertex v is identifiable in n steps if there is a hyperedge containing 
v all of
whose other vertices are identifiable in fewer steps.
   We say that a hyperedge is identifiable if every one of its vertices 
is
identifiable. Our analytic formulae describe the asymptotics of the 
number of
identifiable vertices and the number of identifiable hyperedges for a
Poisson(\beta) random hypergraph \Lambda on a set V of N vertices, in 
the limit
as N\to \infty. Here \beta is a formal power series with nonnegative
coefficients \beta_0,\beta_1,..., and (\Lambda(A))_{A\subseteq V} are
independent Poisson random variables such that \Lambda(A), the number of
hyperedges on A, has mean N\beta_j/\pmatrixN j whenever |A|=j.


http://front.math.ucdavis.edu/math.PR/0503460

---------------------------------------------------------------

3362. LARGE DEVIATIONS FOR TEMPLATE MATCHING BETWEEN POINT PROCESSES

Zhiyi Chi

We study the asymptotics related to the following matching criteria for 
two
independent realizations of point processes X\sim X and Y\sim Y. Given 
l>0,
X\cap [0,l) serves as a template. For each t>0, the matching score 
between the
template and Y\cap [t,t+l) is a weighted sum of the Euclidean distances 
from
y-t to the template over all y\in Y\cap [t,t+l). The template matching 
criteria
are used in neuroscience to detect neural activity with certain 
patterns. We
first consider W_l(\theta), the waiting time until the matching score 
is above
a given threshold \theta. We show that whether the score is scalar- or
vector-valued, (1/l)\log W_l(\theta) converges almost surely to a 
constant
whose explicit form is available, when X is a stationary ergodic 
process and Y
is a homogeneous Poisson point process. Second, as l\to\infty, a strong
approximation for -\log [\Pr{W_l(\theta)=0}] by its rate function is
established, and in the case where X is sufficiently mixing, the rates, 
after
being centered and normalized by \sqrtl, satisfy a central limit 
theorem and
almost sure invariance principle. The explicit form of the variance of 
the
normal distribution is given for the case where X is a homogeneous 
Poisson
process as well.


http://front.math.ucdavis.edu/math.PR/0503463

---------------------------------------------------------------

3363. RANDOM K-SAT: TWO MOMENTS SUFFICE TO CROSS A SHARP THRESHOLD

Dimitris Achlioptas and Cristopher Moore

Many NP-complete constraint satisfaction problems appear to undergo a 
"phase
transition'' from solubility to insolubility when the constraint 
density passes
through a critical threshold. In all such cases it is easy to derive 
upper
bounds on the location of the threshold by showing that above a certain 
density
the first moment (expectation) of the number of solutions tends to 
zero. We
show that in the case of certain symmetric constraints, considering the 
second
moment of the number of solutions yields nearly matching lower bounds 
for the
location of the threshold. Specifically, we prove that the threshold 
for both
random hypergraph 2-colorability (Property B) and random Not-All-Equal 
k-SAT is
2^{k-1} ln 2 -O(1). As a corollary, we establish that the threshold for 
random
k-SAT is of order Theta(2^k), resolving a long-standing open problem.


http://front.math.ucdavis.edu/cond-mat/0310227

---------------------------------------------------------------

3364. DISTRIBUTION OF THE SIZE OF A LARGEST PLANAR MATCHING AND LARGEST 
PLANAR  SUBGRAPH IN RANDOM BIPARTITE GRAPHS

Marcos Kiwi and  Martin Loebl

We address the following question: When a randomly chosen regular 
bipartite
multi--graph is drawn in the plane in the ``standard way'', what is the
distribution of its maximum size planar matching (set of non--crossing 
disjoint
edges) and maximum size planar subgraph (set of non--crossing edges 
which may
share endpoints)? The problem is a generalization of the Longest 
Increasing
Sequence (LIS) problem (also called Ulam's problem). We present 
combinatorial
identities which relate the number of $r$-regular bipartite 
multi--graphs with
maximum planar matching (maximum planar subgraph)of at most $d$ edges 
to a
signed sum of restricted lattice walks in $\ZZ^d$, and to the number of 
pairs
of standard Young tableaux of the same shape and with a 
``descend--type''
property. Our results are obtained via generalizations of two 
combinatorial
proofs through which Gessel's identity can be obtained (an identity 
that is
crucial in the derivation of a bivariate generating function associated 
to the
distribution of LISs, and key to the analytic attack on Ulam's problem).


http://front.math.ucdavis.edu/math.CO/0503465

---------------------------------------------------------------

3365. THE SHANNON INFORMATION OF FILTRATIONS AND THE ADDITIONAL 
LOGARITHMIC  UTILITY OF INSIDERS

Stefan Ankirchner and  Steffen Dereich and Peter Imkeller

The background for the general mathematical link between utility and
information theory investigated in this paper is a simple financial 
market
model with two kinds of small traders: less informed traders and 
insiders,
whose extra information is represented by an enlargement of the other 
agents'
filtration. The expected logarithmic utility increment, i.e. the 
difference of
the insider's and the less informed trader's expected logarithmic 
utility is
described in terms of the information drift, i.e. the drift one has to
eliminate in order to perceive the price dynamics as a martingale from 
the
insider's perspective. On the one hand, we describe the information 
drift in a
very general setting by natural quantities expressing the probabilistic 
better
informed view of the world. This on the other hand allows us to 
identify the
additional utility by entropy related quantities known from information 
theory.
In particular, in a complete market in which the insider has some fixed
additional information during the entire trading interval, its utility
increment can be represented by the Shannon information of his extra 
knowledge.
For general markets, and in some particular examples, we provide 
estimates of
maximal utility by information inequalities.


http://front.math.ucdavis.edu/math.PR/0503013

---------------------------------------------------------------

3366. DIFFUSION MAPS, SPECTRAL CLUSTERING AND REACTION COORDINATES OF  
DYNAMICAL SYSTEMS

Boaz Nadler and  Stephane Lafon and  Ronald R. Coifman and  Ioannis G. 
Kevrekidis

A central problem in data analysis is the low dimensional 
representation of
high dimensional data, and the concise description of its underlying 
geometry
and density. In the analysis of large scale simulations of complex 
dynamical
systems, where the notion of time evolution comes into play, important 
problems
are the identification of slow variables and dynamically meaningful 
reaction
coordinates that capture the long time evolution of the system. In this 
paper
we provide a unifying view of these apparently different tasks, by 
considering
a family of {\em diffusion maps}, defined as the embedding of complex 
(high
dimensional) data onto a low dimensional Euclidian space, via the 
eigenvectors
of suitably defined random walks defined on the given datasets. 
Assuming that
the data is randomly sampled from an underlying general probability
distribution $p(\x)=e^{-U(\x)}$, we show that as the number of samples 
goes to
infinity, the eigenvectors of each diffusion map converge to the 
eigenfunctions
of a corresponding differential operator defined on the support of the
probability distribution. Different normalizations of the Markov chain 
on the
graph lead to different limiting differential operators. One 
normalization
gives the Fokker-Planck operators with the same potential U(x), best 
suited for
the study of stochastic differential equations as well as for 
clustering.
Another normalization gives the Laplace-Beltrami (heat) operator on the
manifold in which the data resides, best suited for the analysis of the
geometry of the dataset, regardless of its possibly non-uniform density.


http://front.math.ucdavis.edu/math.NA/0503445

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3367. TRADING STRATEGY ADIPTED OPTIMIZATION OF EUROPEAN CALL OPTION

Toshio Fukumi

Optimal pricing of European call option is described by linear 
stochastic
differential equation. Trading strategy given by a twin of stochastic 
variables
was integrated w.r.t. Black-Scholes formula to adopt optimal pricing to
tarading strategy.


http://front.math.ucdavis.edu/math.OC/0503444

---------------------------------------------------------------

3368. CHARACTERIZATION OF ARBITRAGE-FREE MARKETS

Eva Strasser

The present paper deals with the characterization of no-arbitrage 
properties
of a continuous semimartingale. The first main result, Theorem
\refMainTheoremCharNA, extends the no-arbitrage criterion by Levental 
and
Skorohod [Ann. Appl.
   Probab. 5 (1995) 906-925] from diffusion processes to arbitrary 
continuous
semimartingales. The second main result, Theorem 2.4, is a 
characterization of
a weaker notion of no-arbitrage in terms of the existence of 
supermartingale
densities. The pertaining weaker notion of no-arbitrage is equivalent 
to the
absence of immediate arbitrage opportunities, a concept introduced by 
Delbaen
and Schachermayer [Ann. Appl. Probab. 5 (1995) 926-945]. Both results 
are
stated in terms of conditions for any semimartingales starting at 
arbitrary
stopping times \sigma. The necessity parts of both results are known 
for the
stopping time \sigma=0 from Delbaen and Schachermayer [Ann. Appl. 
Probab. 5
(1995) 926-945]. The contribution of the present paper is the proofs of 
the
corresponding sufficiency parts.


http://front.math.ucdavis.edu/math.PR/0503473

---------------------------------------------------------------

3369. GAUSSIAN LIMITS FOR RANDOM MEASURES IN GEOMETRIC PROBABILITY

Yu. Baryshnikov and J. E. Yukich

We establish Gaussian limits for general measures induced by binomial 
and
Poisson point processes in d-dimensional space. The limiting Gaussian 
field has
a covariance functional which depends on the density of the point 
process. The
general results are used to deduce central limit theorems for measures 
induced
by random graphs (nearest neighbor, Voronoi and sphere of influence 
graph),
random sequential packing models (ballistic deposition and spatial 
birth-growth
models) and statistics of germ-grain models.


http://front.math.ucdavis.edu/math.PR/0503474

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3370. ON THE DISTRIBUTION OF THE MAXIMUM OF A GAUSSIAN FIELD WITH D 
PARAMETERS

Jean-Marc Azais and Mario Wschebor

Let I be a compact d-dimensional manifold, let X:I\to R be a Gaussian 
process
with regular paths and let F_I(u), u\in R, be the probability 
distribution
function of sup_{t\in I}X(t). We prove that under certain regularity and
nondegeneracy conditions, F_I is a C^1-function and satisfies a certain
implicit equation that permits to give bounds for its values and to 
compute its
asymptotic behavior as u\to +\infty. This is a partial extension of 
previous
results by the authors in the case d=1. Our methods use strongly the 
so-called
Rice formulae for the moments of the number of roots of an equation of 
the form
Z(t)=x, where Z:I\to R^d is a random field and x is a fixed point in 
R^d. We
also give proofs for this kind of formulae, which have their own 
interest
beyond the present application.


http://front.math.ucdavis.edu/math.PR/0503475

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3371. HEAVY TRAFFIC ANALYSIS OF OPEN PROCESSING NETWORKS WITH COMPLETE  
RESOURCE POOLING: ASYMPTOTIC OPTIMALITY OF DISCRETE REVIEW POLICIES

Baris Ata and Sunil Kumar

We consider a class of open stochastic processing networks, with 
feedback
routing and overlapping server capabilities, in heavy traffic. The 
networks we
consider satisfy the so-called complete resource pooling condition and
therefore have one-dimensional approximating Brownian control problems.
   We propose a simple discrete review policy for controlling such 
networks.
   Assuming 2+\epsilon moments on the interarrival times and processing 
times,
we provide a conceptually simple proof of asymptotic optimality of the 
proposed
policy.


http://front.math.ucdavis.edu/math.PR/0503477

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3372. A CHARACTERIZATION OF THE OPTIMAL RISK-SENSITIVE AVERAGE COST IN 
FINITE  CONTROLLED MARKOV CHAINS

Rolando Cavazos-Cadena and Daniel Hernandez-Hernandez

This work concerns controlled Markov chains with finite state and action
spaces. The transition law satisfies the simultaneous Doeblin 
condition, and
the performance of a control policy is measured by the (long-run)
risk-sensitive average cost criterion associated to a positive, but 
otherwise
arbitrary, risk sensitivity coefficient. Within this context, the 
optimal
risk-sensitive average cost is characterized via a minimization problem 
in a
finite-dimensional Euclidean space.


http://front.math.ucdavis.edu/math.PR/0503478

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3373. LARGE DEVIATIONS OF THE EMPIRICAL VOLUME FRACTION FOR STATIONARY 
POISSON  GRAIN MODELS

Lothar Heinrich

We study the existence of the (thermodynamic) limit of the scaled
cumulant-generating function L_n(z)=|W_n|^{-1}\logE\exp{z|\Xi\cap W_n|} 
of the
empirical volume fraction |\Xi\cap W_n|/|W_n|, where |\cdot| denotes the
d-dimensional Lebesgue measure. Here \Xi=\bigcup_{i\ge1}(\Xi_i+X_i) 
denotes a
d-dimensional Poisson grain model (also known as a Boolean model) 
defined by a
stationary Poisson process \Pi_{\lambda}=\sum_{i\ge1}\delta_{X_i} with
intensity \lambda >0 and a sequence of independent copies 
\Xi_1,\Xi_2,... of a
random compact set \Xi_0. For an increasing family of compact convex 
sets {W_n,
n\ge1} which expand unboundedly in all directions, we prove the 
existence and
analyticity of the limit lim_{n\to\infty}L_n(z) on some disk in the 
complex
plane whenever E\exp{a|\Xi_0|}<\infty for some a>0. Moreover, closely 
connected
with this result, we obtain exponential inequalities and the exact 
asymptotics
for the large deviation probabilities of the empirical volume fraction 
in the
sense of Cram\'er and Chernoff.


http://front.math.ucdavis.edu/math.PR/0503479

From pas at www.economia.unimi.it  Fri Jul  1 13:04:47 2005
From: pas at www.economia.unimi.it (pas@www.economia.unimi.it)
Date: Fri Jul  1 13:06:46 2005
Subject: [Pas] Probabilty Abstrac 87
Message-ID: <95189376-C90C-4129-892F-90DF508905CA@unimi.it>

                                                                         
                          July 1, 2005
                                                                         
                          Letter 87

Probability Abstract Service


---------------------------------------------------------------

3205. RANDOM GRAPHS WITH ARBITRARY I.I.D. DEGREES

Remco van der Hofstad and  Gerard Hooghiemstra and  Dmitri Znamenski

In this paper we study distances and connectivity properties of  
random graphs
with an arbitrary i.i.d. degree sequence. When the tail of the degree
distribution is regularly varying with exponent $1-\tau$ there are three
distinct cases: (i) $\tau>3$, where the degrees have finite variance,  
(ii)
$\tau\in (2,3)$, where the degrees have infinite variance, but finite  
mean, and
(iii) $\tau\in (1,2)$, where the degrees have infinite mean. These  
random
graphs can serve as models for complex networks where degree power  
laws are
observed. The distances between pairs of nodes in the three cases  
mentioned
above have been studied in three previous publications, and we survey  
the
results obtained there. Apart from the critical cases $\tau=1$, $ 
\tau=2$ and
$\tau=3$, this completes the scaling picture. We explain the results
heuristically and describe related work and open problems. We also  
compare the
behavior in this model to Internet data, where a degree power law  
with exponent
$\tau\approx 2.2$ is observed.
   Furthermore, in this paper we derive results concerning the connected
components and the diameter. We give a criterion when there exists a  
unique
largest connected component of size proportional to the size of the  
graph, and
study sizes of the other connected components. Also, we show that for  
$\tau\in
(2,3)$, which is most often observed in real networks, the diameter  
in this
model grows much faster than the typical distance between two  
arbitrary nodes.


http://front.math.ucdavis.edu/math.PR/0502580

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3206. THE SINGLE SERVER QUEUE AND THE STORAGE MODEL: LARGE DEVIATIONS  
AND  FIXED POINTS

Moez Draief

We consider the coupling of a single server queue and a storage model  
defined
as a Queue/Store model in Draief et al. 2004. We establish that if  
the input
variables both arrivals to the queue and to the store satisfy large  
deviations
principles and are linked through an {\em exponential tilting} than  
the output
variables (departures from each system) satisfy large deviations  
principles
with the same rate function. This generalizes to the context of large
deviations the extension of Burke's Theorem derived in Draief et al.  
2004.


http://front.math.ucdavis.edu/math.PR/0503016

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3207. SUBEXPONENTIAL ASYMPTOTICS OF HYBRID FLUID AND RUIN MODELS

Bert Zwart and  Sem Borst and Krzystof Debicki

We investigate the tail asymptotics of the supremum of X(t)+Y(t)-ct,  
where
X={X(t),t\geq 0} and Y={Y(t),t\geq 0} are two independent stochastic  
processes.
We assume that the process Y has subexponential characteristics and  
that the
process X is more regular in a certain sense than Y. A key issue  
examined in
earlier studies is under what conditions the process X contributes to  
large
values of the supremum only through its average behavior. The present  
paper
studies various scenarios where the latter is not the case, and the  
process X
shows some form of ``atypical'' behavior as well. In particular, we  
consider a
fluid model fed by a Gaussian process X and an (integrated) On-Off  
process Y.
We show that, depending on the model parameters, the Gaussian process  
may
contribute to the tail asymptotics by its moderate deviations, large
deviations, or oscillatory behavior.


http://front.math.ucdavis.edu/math.PR/0503482

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3208. DEVIATION INEQUALITIES VIA COUPLING FOR STOCHASTIC PROCESSES  
AND RANDOM  FIELDS

J.-R. Chazottes and  P. Collet and  C. Kuelske and  F. Redig

We present a new and simple approach to deviation inequalities for
non-product measures, i.e., for dependent random variables. Our  
method is based
on coupling. We illustrate our abstract results with chains with  
complete
connections and Gibbsian random fields, both at high and low  
temperature.


http://front.math.ucdavis.edu/math.PR/0503483

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3209. AN APPROXIMATE SAMPLING FORMULA UNDER GENETIC HITCHHIKING

A. M. Etheridge and  P. Pfaffelhuber and A. Wakolbinger

For a genetic locus carrying a strongly beneficial allele which has just
fixed in a large population we study the ancestry at a linked neutral  
locus.
During this ''selective sweep'' the linkage between the two loci is  
broken up
by recombination, and the ancestry at the neutral locus is modelled by a
structured coalescent in a random background. For large selection  
coefficients
$\alpha$ and under an appropriate scaling of the recombination rate,  
we derive
a sampling formula with an order of accuracy of $O((\log\alpha)^{-2}) 
$ in
probability. In particular we see that, with this order of accuracy,  
in a
sample of fixed size there are at most two non-singleton families of
individuals which are identi cal by descent at the neutral locus from  
the
beginning of the sweep. This refines a formula going back to the work of
Maynard Smith and Haigh, and co mplements recent work of Schweinsberg  
and
Durrett on selective sweeps in the Moran model.


http://front.math.ucdavis.edu/math.PR/0503485

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3210. LARGE DEVIATIONS OF A MODIFIED JACKSON NETWORK: STABILITY AND  
ROUGH  ASYMPTOTICS

Robert D. Foley and David R. McDonald

Consider a modified, stable, two node Jackson network where server 2  
helps
server 1 when server 2 is idle. The probability of a large deviation  
of the
number of customers at node one can be calculated using the flat  
boundary
theory of Schwartz and Weiss [Large Deviations Performance Analysis  
(1994),
  Chapman and Hall, New York]. Surprisingly, however, these  
calculations show
that the proportion of time spent on the boundary, where server 2 is  
idle, may
be zero. This is in sharp contrast to the unmodified Jackson network  
which
spends a nonzero proportion of time on this boundary.


http://front.math.ucdavis.edu/math.PR/0503487

---------------------------------------------------------------

3211. BRIDGES AND NETWORKS: EXACT ASYMPTOTICS

Robert D. Foley and David R. McDonald

We extend the Markov additive methodology developed in [Ann. Appl.  
Probab. 9
(1999) 110-145, Ann. Appl. Probab. 11 (2001) 596-607] to obtain the  
sharp
asymptotics of the steady state probability of a queueing network  
when one of
the nodes gets large. We focus on a new phenomenon we call a bridge.  
The bridge
cases occur when the Markovian part of the twisted Markov additive  
process is
one null recurrent or one transient, while the jitter cases treated  
in [Ann.
Appl. Probab. 9 (1999) 110-145, Ann. Appl. Probab. 11 (2001) 596-607]  
occur
when the Markovian part is (one) positive recurrent. The asymptotics  
of the
steady state is an exponential times a polynomial term in the bridge  
case, but
is purely exponential in the jitter case. We apply this theory to a  
modified,
stable, two node Jackson network where server two helps server one  
when server
two is idle. We derive the sharp asymptotics of the steady state  
distribution
of the number of customers queued at each node as the number of  
customers
queued at the server one grows large. In so doing we get an intuitive
understanding of the companion paper [Ann. Appl. Probab. 15 (2005)  
519-541]
which gives a large deviation analysis of this problem using the flat  
boundary
theory in the book by Shwartz and Weiss. Unlike the (unscaled) large  
deviation
path of a Jackson network which jitters along the boundary, the  
unscaled large
deviation path of the modified network tries to avoid the boundary  
where server
two helps server one (and forms a bridge).


http://front.math.ucdavis.edu/math.PR/0503488

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3212. UPPER BOUNDS FOR SPATIAL POINT PROCESS APPROXIMATIONS

Dominic Schuhmacher

We consider the behavior of spatial point processes when subjected to  
a class
of linear transformations indexed by a variable T. It was shown in  
Ellis [Adv.
in Appl. Probab. 18 (1986) 646-659] that, under mild assumptions, the
transformed processes behave approximately like Poisson processes for  
large T.
In this article, under very similar assumptions, explicit upper  
bounds are
given for the d_2-distance between the corresponding point process
distributions. A number of related results, and applications to  
kernel density
estimation and long range dependence testing are also presented. The  
main
results are proved by applying a generalized Stein-Chen method to  
discretized
versions of the point processes.


http://front.math.ucdavis.edu/math.PR/0503491

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3213. NOISE STABILITY OF FUNCTIONS WITH LOW INFLUENCES: INVARIANCE  
AND  OPTIMALITY

Elchanan Mossel and Ryan O'Donnell and Krzysztof Oleszkiewicz

In this paper we study functions with low influences on product  
probability
spaces. The analysis of boolean functions with low influences has  
become a
central problem in discrete Fourier analysis. It is motivated by  
fundamental
questions arising from the construction of probabilistically  
checkable proofs
in theoretical computer science and from problems in the theory of  
social
choice in economics.
   We prove an invariance principle for multilinear polynomials with low
influences and bounded degree; it shows that under mild conditions the
distribution of such polynomials is essentially invariant for all  
product
spaces. Ours is one of the very few known non-linear invariance  
principles. It
has the advantage that its proof is simple and that the error bounds are
explicit. We also show that the assumption of bounded degree can be  
eliminated
if the polynomials are slightly ``smoothed''; this extension is  
essential for
our applications to ``noise stability''-type problems.
   In particular, as applications of the invariance principle we  
prove two
conjectures: the ``Majority Is Stablest'' conjecture from theoretical  
computer
science, which was the original motivation for this work, and the  
``It Ain't
Over Till It's Over'' conjecture from social choice theory.


http://front.math.ucdavis.edu/math.PR/0503503

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3214. LOGARITHMIC SOBOLEV INEQUALITY FOR LOG-CONCAVE MEASURE FROM   
PREKOPA-LEINDLER INEQUALITY

Ivan Gentil

We develop in this paper an amelioration of the method given by S.  
Bobkov and
M. Ledoux in GAFA (2000). We prove by Prekopa-Leindler Theorem an  
optimal
modified logarithmic Sobolev inequality adapted for all log-concave  
measure on
$\dR^n$. This inequality implies results proved by Bobkov and Ledoux,  
the
Euclidean Logarithmic Sobolev inequality generalized in the last  
years and it
also implies some convex logarithmic Sobolev inequalities for large  
entropy.


http://front.math.ucdavis.edu/math.FA/0503476

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3215. EQUILIBRIUM GLAUBER AND KAWASAKI DYNAMICS OF CONTINUOUS  
PARTICLE SYSTEMS

Yu. G. Kondratiev and  E. Lytvynov and  M. R\"ockner

We construct two types of equilibrium dynamics of infinite particle  
systems
in a Riemannian manifold $X$. These dynamics are analogs of the Glauber,
respectively Kawasaki dynamics of lattice spin systems. The Glauber  
dynamics
now is a process where interacting particles randomly appear and  
disappear,
i.e., it is a birth-and-death process in $X$, while in the Kawasaki  
dynamics
interacting particles randomly jump over $X$. We establish conditions  
on a
priori explicitly given symmetrizing measures and generators of both  
dynamics
under which corresponding conservative Markov processes exist.


http://front.math.ucdavis.edu/math.PR/0503042

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3216. THE STEPPING STONE MODEL. II: GENEALOGIES AND THE INFINITE  
SITES MODEL

Iljana Zahle and  J. Theodore Cox and Richard Durrett

This paper extends earlier work by Cox and Durrett, who studied the
coalescence times for two lineages in the stepping stone model on the
two-dimensional torus. We show that the genealogy of a sample of size  
n is
given by a time change of Kingman's coalescent. With DNA sequence  
data in mind,
we investigate mutation patterns under the infinite sites model,  
which assumes
that each mutation occurs at a new site. Our results suggest that the  
spatial
structure of the human population contributes to the haplotype  
structure and a
slower than expected decay of genetic correlation with distance  
revealed by
recent studies of the human genome.


http://front.math.ucdavis.edu/math.PR/0503512

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3217. RENEWAL THEORY AND COMPUTABLE CONVERGENCE RATES FOR  
GEOMETRICALLY  ERGODIC MARKOV CHAINS

Peter H. Baxendale

We give computable bounds on the rate of convergence of the transition
probabilities to the stationary distribution for a certain class of
geometrically ergodic Markov chains. Our results are different from  
earlier
estimates of Meyn and Tweedie, and from estimates using coupling,  
although we
start from essentially the same assumptions of a drift condition  
toward a
``small set.'' The estimates show a noticeable improvement on  
existing results
if the Markov chain is reversible with respect to its stationary  
distribution,
and especially so if the chain is also positive. The method of proof  
uses the
first-entrance-last-exit decomposition, together with new  
quantitative versions
of a result of Kendall from discrete renewal theory.


http://front.math.ucdavis.edu/math.PR/0503515

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3218. UTILITY MAXIMIZATION WITH A STOCHASTIC CLOCK AND AN UNBOUNDED  
RANDOM  ENDOWMENT

Gordan Zitkovic

We introduce a linear space of finitely additive measures to treat the
problem of optimal expected utility from consumption under a  
stochastic clock
and an unbounded random endowment process. In this way we establish  
existence
and uniqueness for a large class of utility-maximization problems  
including the
classical ones of terminal wealth or consumption, as well as the  
problems that
depend on a random time horizon or multiple consumption instances. As an
example we explicitly treat the problem of maximizing the logarithmic  
utility
of a consumption stream, where the local time of an Ornstein- 
Uhlenbeck process
acts as a stochastic clock.


http://front.math.ucdavis.edu/math.PR/0503516

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3219. RECONSTRUCTING A TWO-COLOR SCENERY BY OBSERVING IT ALONG A  
SIMPLE RANDOM  WALK PATH

Heinrich Matzinger

Let {\xi (n)}_{n\in Z} be a two-color random scenery, that is, a random
coloring of Z in two colors, such that the \xi (i)'s are i.i.d.  
Bernoulli
variables with parameter \tfrac12. Let {S(n)}_{n\in N} be a symmetric  
random
walk starting at 0. Our main result shows that a.s., \xi \circ S (the
composition of \xi and S) determines \xi up to translation and  
reflection. In
other words, by observing the scenery \xi along the random walk path  
S, we can
a.s. reconstruct \xi up to translation and reflection. This result  
gives a
positive answer to the question of H. Kesten of whether one can a.s.  
detect a
single defect in almost every two-color random scenery by observing  
it only
along a random walk path.


http://front.math.ucdavis.edu/math.PR/0503517

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3220. A DIFFUSION MODEL OF SCHEDULING CONTROL IN QUEUEING SYSTEMS  
WITH MANY  SERVERS

Rami Atar

This paper studies a diffusion model that arises as the limit of a  
queueing
system scheduling problem in the asymptotic heavy traffic regime of  
Halfin and
Whitt. The queueing system consists of several customer classes and many
servers working in parallel, grouped in several stations. Servers in  
different
stations offer service to customers of each class at possibly  
different rates.
The control corresponds to selecting what customer class each server  
serves at
each time. The diffusion control problem does not seem to have explicit
solutions and therefore a characterization of optimal solutions via the
Hamilton-Jacobi-Bellman equation is addressed. Our main result is the  
existence
and uniqueness of solutions of the equation. Since the model is set  
on an
unbounded domain and the cost per unit time is unbounded, the  
analysis requires
estimates on the state process that are subexponential in the time  
variable. In
establishing these estimates, a key role is played by an integral  
formula that
relates queue length and idle time processes, which may be of  
independent
interest.


http://front.math.ucdavis.edu/math.PR/0503518

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3221. EXACT AND APPROXIMATE RESULTS FOR DEPOSITION AND ANNIHILATION  
PROCESSES  ON GRAPHS

Mathew D. Penrose and Aidan Sudbury

We consider random sequential adsorption processes where the  
initially empty
sites of a graph are irreversibly occupied, in random order, either  
by monomers
which block neighboring sites, or by dimers. We also consider a  
process where
initially occupied sites annihilate their neighbors at random times.  
We verify
that these processes are well defined on infinite graphs, and derive  
forward
equations governing joint vacancy/occupation probabilities. Using  
these, we
derive exact formulae for occupation probabilities and pair  
correlations in
Bethe lattices. For the blocking and annihilation processes we also  
prove
positive correlations between sites an even distance apart, and for  
blocking we
derive rigorous lower bounds for the site occupation probability in  
lattices,
including a lower bound of 1/3 for Z^2. We also give normal  
approximation
results for the number of occupied sites in a large finite graph.


http://front.math.ucdavis.edu/math.PR/0503519

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3222. NEAR-INTEGRATED GARCH SEQUENCES

Istvan Berkes and  Lajos Horvath and Piotr Kokoszka

Motivated by regularities observed in time series of returns on  
speculative
assets, we develop an asymptotic theory of GARCH(1,1) processes {y_k}  
defined
by the equations y_k=\sigma_k\epsilon_k, \sigma_k^2=\omega +\alpha
y_{k-1}^2+\beta \sigma_{k-1}^2 for which the sum \alpha +\beta  
approaches unity
as the number of available observations tends to infinity. We call such
sequences near-integrated. We show that the asymptotic behavior of
near-integrated GARCH(1,1) processes critically depends on the sign  
of \gamma
:=\alpha +\beta -1. We find assumptions under which the solutions  
exhibit
increasing oscillations and show that these oscillations grow  
approximately
like a power function if \gamma \leq 0 and exponentially if \gamma  
 >0. We
establish an additive representation for the near-integrated GARCH(1,1)
processes which is more convenient to use than the traditional  
multiplicative
Volterra series expansion.


http://front.math.ucdavis.edu/math.PR/0503520

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3223. ASYMPTOTICS IN RANDOMIZED URN MODELS

Zhi-Dong Bai and Feifang Hu

This paper studies a very general urn model stimulated by designs in  
clinical
trials, where the number of balls of different types added to the urn  
at trial
n depends on a random outcome directed by the composition at trials
1,2,...,n-1. Patient treatments are allocated according to types of  
balls. We
establish the strong consistency and asymptotic normality for both  
the urn
composition and the patient allocation under general assumptions on  
random
generating matrices which determine how balls are added to the urn.  
Also we
obtain explicit forms of the asymptotic variance-covariance matrices  
of both
the urn composition and the patient allocation. The conditions on the
nonhomogeneity of generating matrices are mild and widely satisfied in
applications. Several applications are also discussed.


http://front.math.ucdavis.edu/math.PR/0503521

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3224. A BERRY-ESSEEN THEOREM FOR FEYNMAN-KAC AND INTERACTING PARTICLE  
MODELS

Pierre Del Moral and Samy Tindel

In this paper we investigate the speed of convergence of the  
fluctuations of
a general class of Feynman-Kac particle approximation models. We  
design an
original approach based on new Berry-Esseen type estimates for abstract
martingale sequences combined with original exponential concentration  
estimates
of interacting processes. These results extend the corresponding  
statements in
the classical theory and apply to a class of branching and genealogical
path-particle models arising in nonlinear filtering literature as  
well as in
statistical physics and biology.


http://front.math.ucdavis.edu/math.PR/0503522

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3225. PERIODIC COPOLYMERS AT SELECTIVE INTERFACES: A LARGE DEVIATIONS  
APPROACH

Erwin Bolthausen and Giambattista Giacomin

We analyze a (1+1)-dimension directed random walk model of a polymer  
dipped
in a medium constituted by two immiscible solvents separated by a flat
interface. The polymer chain is heterogeneous in the sense that a single
monomer may energetically favor one or the other solvent. We focus on  
the case
in which the polymer types are periodically distributed along the  
chain or, in
other words, the polymer is constituted of identical stretches of  
fixed length.
The phenomenon that one wants to analyze is the localization at the  
interface:
energetically favored configurations place most of the monomers in the
preferred solvent and this can be done only if the polymer sticks  
close to the
interface. We investigate, by means of large deviations, the energy- 
entropy
competition that may lead, according to the value of the parameters (the
strength of the coupling between monomers and solvents and an asymmetry
parameter), to localization. We express the free energy of the system  
in terms
of a variational formula that we can solve. We then use the result to  
analyze
the phase diagram.


http://front.math.ucdavis.edu/math.PR/0503523

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3226. HITTING DISTRIBUTIONS OF GEOMETRIC BROWNIAN MOTION

T. Byczkowski and M. Ryznar

Let $\tau$ be the first hitting time of the point 1 by the geometric  
Brownian
motion $X(t)= x \exp(B(t)-2\mu t)$ with drift $\mu \geq 0$ starting  
from $x>1$.
Here $B(t)$ is the Brownian motion starting from 0 with $E^0 B^2(t) =  
2t$. We
provide an integral formula for the density function of the stopped  
exponential
functional $A(\tau)=\int_0^\tau X^2(t) dt$ and determine its asymptotic
behaviour at infinity. Although we basically rely on methods  
developed in
\cite{BGS}, the present paper also covers the case of arbitrary  
drifts $\mu
\geq 0$ and provides a significant unification and extension of  
results of the
above-mentioned paper. As a corollary we provide an integral formula  
and give
asymptotic behaviour at infinity of the Poisson kernel for half- 
spaces for
Brownian motion with drift in real hyperbolic spaces of arbitrary  
dimension.


http://front.math.ucdavis.edu/math.PR/0503060

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3227. MASS EXTINCTIONS: AN ALTERNATIVE TO THE ALLEE EFFECT

Rinaldo B. Schinazi

We introduce a spatial stochastic process on the lattice Z^d to model  
mass
extinctions. Each site of the lattice may host a flock of up to N  
individuals.
Each individual may give birth to a new individual at the same site  
at rate
\phi until the maximum of N individuals has been reached at the site.  
Once the
flock reaches N individuals, then, and only then, it starts giving  
birth on
each of the 2d neighboring sites at rate \lambda(N). Finally,  
disaster strikes
at rate 1, that is, the whole flock disappears. Our model shows that,  
at least
in theory, there is a critical maximum flock size above which a  
species is
certain to disappear and below which it may survive.


http://front.math.ucdavis.edu/math.PR/0503525

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3228. TAIL OF A LINEAR DIFFUSION WITH MARKOV SWITCHING

Benoite de Saporta and Jian-Feng Yao

Let Y be an Ornstein-Uhlenbeck diffusion governed by a stationary and  
ergodic
Markov jump process X: dY_t=a(X_t)Y_t dt+\sigma(X_t) dW_t, Y_0=y_0.  
Ergodicity
conditions for Y have been obtained. Here we investigate the tail  
propriety of
the stationary distribution of this model. A characterization of  
either heavy
or light tail case is established. The method is based on a renewal  
theorem for
systems of equations with distributions on R.


http://front.math.ucdavis.edu/math.PR/0503527

---------------------------------------------------------------

3229. THE LONG-RUN BEHAVIOR OF THE STOCHASTIC REPLICATOR DYNAMICS

Lorens A. Imhof

Fudenberg and Harris' stochastic version of the classical replicator  
dynamics
is considered. The behavior of this diffusion process in the presence  
of an
evolutionarily stable strategy is investigated. Moreover, extinction of
dominated strategies and stochastic stability of strict Nash  
equilibria are
studied. The general results are illustrated in connection with a  
discrete war
of attrition. A persistence result for the maximum effort strategy is  
obtained
and an explicit expression for the evolutionarily stable strategy is  
derived.


http://front.math.ucdavis.edu/math.PR/0503529

---------------------------------------------------------------

3230. OPTIMAL POINTWISE APPROXIMATION OF SDES BASED ON BROWNIAN  
MOTION AT  DISCRETE POINTS

Thomas Muller-Gronbach

We study pathwise approximation of scalar stochastic differential  
equations
at a single point. We provide the exact rate of convergence of the  
minimal
errors that can be achieved by arbitrary numerical methods that are  
based (in a
measurable way) on a finite number of sequential observations of the  
driving
Brownian motion. The resulting lower error bounds hold in particular  
for all
methods that are implementable on a computer and use a random number  
generator
to simulate the driving Brownian motion at finitely many points. Our  
analysis
shows that approximation at a single point is strongly connected to an
integration problem for the driving Brownian motion with a random  
weight.
Exploiting general ideas from estimation of weighted integrals of  
stochastic
processes, we introduce an adaptive scheme, which is easy to  
implement and
performs asymptotically optimally.


http://front.math.ucdavis.edu/math.PR/0503531

---------------------------------------------------------------

3231. QUANTITATIVE BOUNDS ON CONVERGENCE OF TIME-INHOMOGENEOUS MARKOV  
CHAINS

R. Douc and  E. Moulines and Jeffrey S. Rosenthal

Convergence rates of Markov chains have been widely studied in recent  
years.
In particular, quantitative bounds on convergence rates have been  
studied in
various forms by Meyn and Tweedie [Ann. Appl. Probab. 4 (1994)  
981-1101],
Rosenthal [J. Amer. Statist. Assoc. 90 (1995) 558-566], Roberts and  
Tweedie
[Stochastic Process. Appl. 80 (1999) 211-229], Jones and Hobert  
[Statist. Sci.
16 (2001) 312-334] and Fort [Ph.D. thesis (2001) Univ. Paris VI]. In  
this
paper, we extend a result of Rosenthal [J. Amer. Statist. Assoc. 90  
(1995)
558-566] that concerns quantitative convergence rates for time- 
homogeneous
Markov chains. Our extension allows us to consider f-total variation  
distance
(instead of total variation) and time-inhomogeneous Markov chains. We  
apply our
results to simulated annealing.


http://front.math.ucdavis.edu/math.PR/0503532

---------------------------------------------------------------

3232. ON STATIONARITY OF LAGRANGIAN OBSERVATIONS OF PASSIVE TRACER  
VELOCITY IN  A COMPRESSIBLE ENVIRONMENT

Tomasz Komorowski and Grzegorz Krupa

We study the transport of a passive tracer particle in a steady strongly
mixing flow with a nonzero mean velocity. We show that there exists a
probability measure under which the particle Lagrangian velocity  
process is
stationary. This measure is absolutely continuous with respect to the
underlying probability measure for the Eulerian flow.


http://front.math.ucdavis.edu/math.PR/0503534

---------------------------------------------------------------

3233. EXTENDING CHACON-WALSH: MINIMALITY AND GENERALISED STARTING   
DISTRIBUTIONS

Alexander Cox

In this paper we consider the Skorokhod embedding problem for general
starting and target measures. In particular, we provide necessary and
sufficient conditions for a stopping time to be minimal in the sense of
Monroe(1972). The resulting conditions have a nice interpretation in the
graphical picture of Chacon and Walsh. Further, we demonstrate how the
construction of Chacon and Walsh can be extended to any (integrable)  
starting
and target distributions, allowing the constructions of Azema-Yor,  
Vallois and
Jacka to be viewed in this context, and thus extended easily to general
starting and target distributions. In particular, we describe in  
detail the
extension of the Azema-Yor embedding in this context, and show that  
it retains
its optimality property.


http://front.math.ucdavis.edu/math.PR/0503535

---------------------------------------------------------------

3234. EXPONENTIAL PENALTY FUNCTION CONTROL OF LOSS NETWORKS

Garud Iyengar and Karl Sigman

We introduce penalty-function-based admission control policies to
approximately maximize the expected reward rate in a loss network. These
control policies are easy to implement and perform well both in the  
transient
period as well as in steady state. A major advantage of the penalty  
approach is
that it avoids solving the associated dynamic program. However, a  
disadvantage
of this approach is that it requires the capacity requested by  
individual
requests to be sufficiently small compared to total available  
capacity. We
first solve a related deterministic linear program (LP) and then  
translate an
optimal solution of the LP into an admission control policy for the loss
network via an exponential penalty function. We show that the penalty  
policy is
a target-tracking policy--it performs well because the optimal  
solution of the
LP is a good target. We demonstrate that the penalty approach can be  
extended
to track arbitrarily defined target sets. Results from preliminary  
simulation
studies are included.


http://front.math.ucdavis.edu/math.PR/0503536

---------------------------------------------------------------

3235. ELEMENTARY BOUNDS ON POINCARE AND LOG-SOBOLEV CONSTANTS FOR  
DECOMPOSABLE  MARKOV CHAINS

Mark Jerrum and  Jung-Bae Son and  Prasad Tetali and Eric Vigoda

We consider finite-state Markov chains that can be naturally  
decomposed into
smaller ``projection'' and ``restriction'' chains. Possibly this  
decomposition
will be inductive, in that the restriction chains will be smaller  
copies of the
initial chain. We provide expressions for Poincare (resp. log-Sobolev)
constants of the initial Markov chain in terms of Poincare (resp. log- 
Sobolev)
constants of the projection and restriction chains, together with  
further a
parameter. In the case of the Poincare constant, our bound is always  
at least
as good as existing ones and, depending on the value of the extra  
parameter,
may be much better. There appears to be no previously published  
decomposition
result for the log-Sobolev constant. Our proofs are elementary and
self-contained.


http://front.math.ucdavis.edu/math.PR/0503537

---------------------------------------------------------------

3236. RUIN PROBABILITIES AND OVERSHOOTS FOR GENERAL LEVY INSURANCE  
RISK  PROCESSES

Claudia Kluppelberg and  Andreas E. Kyprianou and Ross A. Maller

We formulate the insurance risk process in a general Levy process  
setting,
and give general theorems for the ruin probability and the asymptotic
distribution of the overshoot of the process above a high level, when  
the
process drifts to -\infty a.s. and the positive tail of the Levy  
measure, or of
the ladder height measure, is subexponential or, more generally,  
convolution
equivalent. Results of Asmussen and Kluppelberg [Stochastic Process.  
Appl. 64
(1996) 103-125] and Bertoin and Doney [Adv. in Appl. Probab. 28  
(1996) 207-226]
for ruin probabilities and the overshoot in random walk and compound  
Poisson
models are shown to have analogues in the general setup. The  
identities we
derive open the way to further investigation of general renewal-type  
properties
of Levy processes.


http://front.math.ucdavis.edu/math.PR/0503539

---------------------------------------------------------------

3237. COMBINATORIAL ASPECTS OF MATRIX MODELS

Alice Guionnet and \'Edouard Maurel-Segala

We show that under reasonably general assumptions, the first order
asymptotics of the free energy of matrix models are generating  
functions for
colored planar maps. This is based on the fact that solutions of the
differential Schwinger-Dyson equations are, by nature, generating  
functions for
enumerating planar maps, a remark which bypasses the use of Gaussian  
calculus.


http://front.math.ucdavis.edu/math.PR/0503064

---------------------------------------------------------------

3238. STABILITY IN DISTRIBUTION OF RANDOMLY PERTURBED QUADRATIC MAPS  
AS MARKOV  PROCESSES

Rabi Bhattacharya and Mukul Majumdar

Iteration of randomly chosen quadratic maps defines a Markov process:
X_{n+1}=\epsilon_{n+1}X_n(1-X_n), where \epsilon_n are i.i.d. with  
values in
the parameter space [0,4] of quadratic maps F_{\theta}(x)=\theta x(1- 
x). Its
study is of significance as an important Markov model, with  
applications to
problems of optimization under uncertainty arising in economics. In this
article a broad criterion is established for positive Harris  
recurrence of X_n.


http://front.math.ucdavis.edu/math.PR/0503540

---------------------------------------------------------------

3239. INTERPLAY BETWEEN DIVIDEND RATE AND BUSINESS CONSTRAINTS FOR A  
FINANCIAL  CORPORATION

Tahir Choulli and  Michael Taksar and Xun Yu Zhou

We study a model of a corporation which has the possibility to choose  
various
production/business policies with different expected profits and  
risks. In the
model there are restrictions on the dividend distribution rates as  
well as
restrictions on the risk the company can undertake. The objective is to
maximize the expected present value of the total dividend  
distributions. We
outline the corresponding Hamilton-Jacobi-Bellman equation, compute  
explicitly
the optimal return function and determine the optimal policy. As a  
consequence
of these results, the way the dividend rate and business constraints  
affect the
optimal policy is revealed. In particular, we show that under certain
relationships between the constraints and the exogenous parameters of  
the
random processes that govern the returns, some business activities  
might be
redundant, that is, under the optimal policy they will never be used  
in any
scenario.


http://front.math.ucdavis.edu/math.PR/0503541

---------------------------------------------------------------

3240. LIMIT THEOREMS FOR MIXED MAX-SUM PROCESSES WITH RENEWAL STOPPING

Dmitrii S. Silvestrov and Jozef L. Teugels

This article is devoted to the investigation of limit theorems for mixed
max-sum processes with renewal type stopping indexes. Limit theorems  
of weak
convergence type are obtained as well as functional limit theorems.


http://front.math.ucdavis.edu/math.PR/0503543

---------------------------------------------------------------

3241. CONTINUUM PERCOLATION WITH STEPS IN AN ANNULUS

Paul Balister and  Bela Bollobas and Mark Walters

Let A be the annulus in R^2 centered at the origin with inner and  
outer radii
r(1-\epsilon) and r, respectively. Place points {x_i} in R^2  
according to a
Poisson process with intensity 1 and let G_A be the random graph with  
vertex
set {x_i} and edges x_ix_j whenever x_i-x_j\in A. We show that if the  
area of A
is large, then G_A almost surely has an infinite component. Moreover,  
if we fix
\epsilon, increase r and let n_c=n_c(\epsilon) be the area of A when  
this
infinite component appears, then n_c\to1 as \epsilon \to 0. This is  
in contrast
to the case of a ``square'' annulus where we show that n_c is bounded  
away from
1.


http://front.math.ucdavis.edu/math.PR/0503544

---------------------------------------------------------------

3242. A MICROSCOPIC PROBABILISTIC DESCRIPTION OF A LOCALLY REGULATED   
POPULATION AND MACROSCOPIC APPROXIMATIONS

Nicolas Fournier and Sylvie Meleard

We consider a discrete model that describes a locally regulated spatial
population with mortality selection. This model was studied in  
parallel by
Bolker and Pacala and Dieckmann, Law and Murrell. We first generalize  
this
model by adding spatial dependence. Then we give a pathwise  
description in
terms of Poisson point measures. We show that different  
normalizations may lead
to different macroscopic approximations of this model. The first  
approximation
is deterministic and gives a rigorous sense to the number density.  
The second
approximation is a superprocess previously studied by Etheridge.  
Finally, we
study in specific cases the long time behavior of the system and of its
deterministic approximation.


http://front.math.ucdavis.edu/math.PR/0503546

---------------------------------------------------------------

3243. STABILITY AND THE LYAPOUNOV EXPONENT OF THRESHOLD AR-ARCH MODELS

Daren B. H. Cline and Huay-min H. Pu

The Lyapounov exponent and sharp conditions for geometric ergodicity are
determined of a time series model with both a threshold  
autoregression term and
threshold autoregressive conditional heteroscedastic (ARCH) errors.
  The conditions require studying or simulating the behavior of a  
bounded,
ergodic Markov chain. The method of proof is based on a new approach,  
called
the piggyback method, that exploits the relationship between the time  
series
and the bounded chain. The piggyback method also provides a means for
evaluating the Lyapounov exponent by simulation and provides a new  
perspective
on moments, illuminating recent results for the distribution tails of  
GARCH
models.


http://front.math.ucdavis.edu/math.PR/0503547

---------------------------------------------------------------

3244. NORMAL APPROXIMATION FOR HIERARCHICAL STRUCTURES

Larry Goldstein

Given F:[a,b]^k\to [a,b] and a nonconstant X_0 with P(X_0\in [a,b]) 
=1, define
the hierarchical sequence of random variables {X_n}_{n\ge 0} by
X_{n+1}=F(X_{n,1},...,X_{n,k}), where X_{n,i} are i.i.d. as X_n. Such  
sequences
arise from hierarchical structures which have been extensively  
studied in the
physics literature to model, for example, the conductivity of a  
random medium.
Under an averaging and smoothness condition on nontrivial F, an upper  
bound of
the form C\gamma^n for 0<\gamma<1 is obtained on the Wasserstein  
distance
between the standardized distribution of X_n and the normal. The  
results apply,
for instance, to random resistor networks and, introducing the notion  
of strict
averaging, to hierarchical sequences generated by certain  
compositions. As an
illustration, upper bounds on the rate of convergence to the normal  
are derived
for the hierarchical sequence generated by the weighted diamond  
lattice which
is shown to exhibit a full range of convergence rate behavior.


http://front.math.ucdavis.edu/math.PR/0503549

---------------------------------------------------------------

3245. ON THE SUPER REPLICATION PRICE OF UNBOUNDED CLAIMS

Sara Biagini and Marco Frittelli

In an incomplete market the price of a claim f in general cannot be  
uniquely
identified by no arbitrage arguments. However, the ``classical'' super
replication price is a sensible indicator of the (maximum selling)  
value of the
claim. When f satisfies certain pointwise conditions (e.g., f is  
bounded from
below), the super replication price is equal to sup_QE_Q[f], where Q  
varies on
the whole set of pricing measures. Unfortunately, this price is often  
too high:
a typical situation is here discussed in the examples. We thus define  
the less
expensive weak super replication price and we relax the requirements  
on f by
asking just for ``enough'' integrability conditions. By building up a  
proper
duality theory, we show its economic meaning and its relation with the
investor's preferences. Indeed, it turns out that the weak super  
replication
price of f coincides with sup_{Q\in M_{\Phi}}E_Q[f], where M_{\Phi}  
is the
class of pricing measures with finite generalized entropy (i.e., E[\Phi
(\frac{dQ}{dP})]<\infty) and where \Phi is the convex conjugate of  
the utility
function of the investor.


http://front.math.ucdavis.edu/math.PR/0503550

---------------------------------------------------------------

3246. LIMIT LAWS OF ESTIMATORS FOR CRITICAL MULTI-TYPE GALTON-WATSON  
PROCESSES

Zhiyi Chi

We consider the asymptotics of various estimators based on a large  
sample of
branching trees from a critical multi-type Galton-Watson process, as  
the sample
size increases to infinity. The asymptotics of additive functions of  
trees,
such as sizes of trees and frequencies of types within trees, a  
higher-order
asymptotic of the ``relative frequency'' estimator of the left  
eigenvector of
the mean matrix, a higher-order joint asymptotic of the maximum  
likelihood
estimators of the offspring probabilities and the consistency of an  
estimator
of the right eigenvector of the mean matrix, are established.


http://front.math.ucdavis.edu/math.PR/0503552

---------------------------------------------------------------

3247. ON SAMPLING OF STATIONARY INCREMENT PROCESSES

J. M. P. Albin

Under a complex technical condition, similar to such used in extreme  
value
theory, we find the rate q(\epsilon)^{-1} at which a stochastic  
process with
stationary increments \xi should be sampled, for the sampled process
\xi(\lfloor\cdot /q(\epsilon)\rfloor q(\epsilon)) to deviate from \xi  
by at
most \epsilon, with a given probability, asymptotically as \epsilon
\downarrow0. The canonical application is to discretization errors in  
computer
simulation of stochastic processes.


http://front.math.ucdavis.edu/math.PR/0503554

---------------------------------------------------------------

3248. RECURRENCE OF SIMPLE RANDOM WALK ON $Z^2$ IS DYNAMICALLY SENSITIVE

Christopher Hoffman

Benjamini, Haggstrom, Peres and Steif introduced the concept of a  
dynamical
random walk. This is a continuous family of random walks, {S_n(t)}.  
Benjamini
et. al. proved that if d=3 or d=4 then there is an exceptional set of  
t such
that {S_n(t)} returns to the origin infinitely often. In this paper  
we consider
a dynamical random walk on Z^2. We show that with probability one  
there exists
t such that {S_n(t)} never returns to the origin. This exceptional  
set of times
has dimension one. This proves a conjecture of Benjamini et. al.


http://front.math.ucdavis.edu/math.PR/0503065

---------------------------------------------------------------

3249. SPECTRAL PROPERTIES OF THE TANDEM JACKSON NETWORK, SEEN AS A   
QUASI-BIRTH-AND-DEATH PROCESS

D. P. Kroese and  W. R. W. Scheinhardt and P. G. Taylor

Quasi-birth-and-death (QBD) processes with infinite ``phase spaces'' can
exhibit unusual and interesting behavior. One of the simplest  
examples of such
a process is the two-node tandem Jackson network, with the ``phase''  
giving the
state of the first queue and the ``level'' giving the state of the  
second
queue. In this paper, we undertake an extensive analysis of the  
properties of
this QBD. In particular, we investigate the spectral properties of  
Neuts's
R-matrix and show that the decay rate of the stationary distribution  
of the
``level'' process is not always equal to the convergence norm of R.  
In fact, we
show that we can obtain any decay rate from a certain range by  
controlling only
the transition structure at level zero, which is independent of R. We  
also
consider the sequence of tandem queues that is constructed by  
restricting the
waiting room of the first queue to some finite capacity, and then  
allowing this
capacity to increase to infinity. We show that the decay rates for  
the finite
truncations converge to a value, which is not necessarily the decay  
rate in the
infinite waiting room case. Finally, we show that the probability  
that the
process hits level n before level 0 given that it starts in level 1  
decays at a
rate which is not necessarily the same as the decay rate for the  
stationary
distribution.


http://front.math.ucdavis.edu/math.PR/0503555

---------------------------------------------------------------

3250. NUMBER OF PATHS VERSUS NUMBER OF BASIS FUNCTIONS IN AMERICAN  
OPTION  PRICING

Paul Glasserman and Bin Yu

An American option grants the holder the right to select the time at  
which to
exercise the option, so pricing an American option entails solving an  
optimal
stopping problem. Difficulties in applying standard numerical methods to
complex pricing problems have motivated the development of techniques  
that
combine Monte Carlo simulation with dynamic programming. One class of  
methods
approximates the option value at each time using a linear combination  
of basis
functions, and combines Monte Carlo with backward induction to  
estimate optimal
coefficients in each approximation. We analyze the convergence of  
such a method
as both the number of basis functions and the number of simulated paths
increase. We get explicit results when the basis functions are  
polynomials and
the underlying process is either Brownian motion or geometric  
Brownian motion.
We show that the number of paths required for worst-case convergence  
grows
exponentially in the degree of the approximating polynomials in the  
case of
Brownian motion and faster in the case of geometric Brownian motion.


http://front.math.ucdavis.edu/math.PR/0503556

---------------------------------------------------------------

3251. STOCHASTIC CHARACTERIZATION OF HARMONIC MAPS ON RIEMANNIAN  
POLYHEDRA

M. A. Aprodu and  T. Bouziane

The aim of this paper is to relate the theory of Harmonicity in sense
Korevaar-Schoen and Eells-Fuglede to the notion of a Brownian motion in
riemannian polyhedra achieved by the second author. Firstly, we prove  
that
Brownian motions is stochastically continuous Markov processes and  
consequently
it has a unique infinitesimal generator on some Banach space.  
Secondly, we show
that in some sense, the Brownian motion in Riemannian polyhedra has  
as an
infinitesimal generator the "Laplacian". Finally, we show that  
harmonic maps,
with target smooth Riemannian manifolds, in the sense of Eells- 
Fuglede, are
exactly those which maps Brownian motion in Riemannian polyhedron into a
martingale, while harmonic morphisms are exactly the maps which are  
Brownian
preserving paths


http://front.math.ucdavis.edu/math.PR/0503557

---------------------------------------------------------------

3252. CENTRAL LIMIT THEOREMS FOR RANDOM POLYTOPES IN A SMOOTH CONVEX SET

Van Vu

Let $K$ be a smooth convex set with volume one in $\BBR^d$. Choose $n 
$ random
points in $K$ independently according to the uniform distribution.  
The convex
hull of these points, denoted by $K_n$, is called a {\it random  
polytope}. We
prove that several key functionals of $K_n$ satisfy the central limit  
theorem
as $n$ tends to infinity.


http://front.math.ucdavis.edu/math.PR/0503559

---------------------------------------------------------------

3253. QUENCHED INVARIANCE PRINCIPLE FOR SIMPLE RANDOM WALK ON TWO- 
DIMENSIONAL  PERCOLATION CLUSTERS

Noam Berger and Marek Biskup

We consider the simple random walk on a two-dimensional super-critical
infinite percolation cluster and prove that for almost every  
configuration it
scales to Brownian motion.


http://front.math.ucdavis.edu/math.PR/0503576

---------------------------------------------------------------

3254. ASYMPTOTIC GENEALOGY OF A CRITICAL BRANCHING PROCESS

Lea Popovic

Consider a continuous-time binary branching process conditioned to have
population size n at some time t, and with a chance p for recording each
extinct individual in the process. Within the family tree of this  
process, we
consider the smallest subtree containing the genealogy of the extant
individuals together with the genealogy of the recorded extinct  
individuals. We
introduce a novel representation of such subtrees in terms of a point- 
process,
and provide asymptotic results on the distribution of this point- 
process as the
number of extant individuals increases. We motivate the study within  
the scope
of a coherent analysis for an a priori model for macroevolution.


http://front.math.ucdavis.edu/math.PR/0503577

---------------------------------------------------------------

3255. GENERALIZED STOCHASTIC DIFFERENTIAL UTILITY AND PREFERENCE FOR   
INFORMATION

Ali Lazrak

This paper develops, in a Brownian information setting, an approach for
analyzing the preference for information, a question that motivates the
stochastic differential utility (SDU) due to Duffie and Epstein  
[Econometrica
60 (1992) 353-394]. For a class of backward stochastic differential  
equations
(BSDEs) including the generalized SDU [Lazrak and Quenez Math. Oper.  
Res. 28
(2003) 154-180], we formulate the information neutrality property as an
invariance principle when the filtration is coarser (or finer) and  
characterize
it. We also provide concrete examples of heterogeneity in information  
that
illustrate explicitly the nonneutrality property for some GSDUs. Our  
results
suggest that, within the GSDUs class of intertemporal utilities, risk  
aversion
or ambiguity aversion are inflexibly linked to the preference for  
information.


http://front.math.ucdavis.edu/math.PR/0503579

---------------------------------------------------------------

3256. THE RIGHT TIME TO SELL A STOCK WHOSE PRICE IS DRIVEN BY  
MARKOVIAN NOISE

Robert C. Dalang and M.-O. Hongler

We consider the problem of finding the optimal time to sell a stock,  
subject
to a fixed sales cost and an exponential discounting rate \rho. We  
assume that
the price of the stock fluctuates according to the equation dY_t=Y_t(\mu
dt+\sigma\xi(t) dt), where (\xi(t)) is an alternating Markov renewal  
process
with values in {\pm1}, with an exponential renewal time. We determine  
the
critical value of \rho under which the value function is finite. We  
examine the
validity of the ``principle of smooth fit'' and use this to give a  
complete and
essentially explicit solution to the problem, which exhibits a  
surprisingly
rich structure. The corresponding result when the stock price evolves  
according
to the Black and Scholes model is obtained as a limit case.


http://front.math.ucdavis.edu/math.PR/0503580

---------------------------------------------------------------

3257. CONCENTRATION OF NORMALIZED SUMS AND A CENTRAL LIMIT THEOREM  
FOR  NONCORRELATED RANDOM VARIABLES

Sergey G. Bobkov

For noncorrelated random variables, we study a concentration property  
of the
family of distributions of normalized sums formed by sequences of  
times of a
given large length.


http://front.math.ucdavis.edu/math.PR/0503583

---------------------------------------------------------------

3258. ANALYSIS OF A CLASS OF LIKELIHOOD BASED CONTINUOUS TIME  
STOCHASTIC  VOLATILITY MODELS INCLUDING ORNSTEIN-UHLENBECK MODELS IN  
FINANCIAL ECONOMICS

Lancelot F. James

In a series of recent papers Barndorff-Nielsen and Shephard introduce an
attractive class of continuous time stochastic volatility models for  
financial
assets where the volatility processes are functions of positive
Ornstein-Uhlenbeck(OU) processes. This models are known to be  
substantially
more flexible than Gaussian based models. One current problem of this  
approach
is the unavailability of a tractable exact analysis of likelihood based
stochastic volatility models for the returns of log prices of stocks.
   With this point in mind, the likelihood models of Barndorff- 
Nielsen and
Shephard are viewed as members of a much larger class of models. That is
likelihoods based on n conditionally independent Normal random  
variables whose
mean and variance are representable as linear functionals of a common
unobserved Poisson random measure. The analysis of these models is  
facilitated
by applying the methods in James (2005, 2002), in particular an  
Esscher type
transform of Poisson random measures; in conjunction with a special  
case of the
Weber-Sonine formula. It is shown that the marginal likelihood may be  
expressed
in terms of a multidimensional Fourier-cosine transform. This yields  
tractable
forms of the likelihood and also allows a full Bayesian posterior  
analysis of
the integrated volatility process. A general formula for the  
posterior density
of the log price given the observed data is derived, which could  
potentially
have applications to option pricing. We also identify tractable  
subclasses,
where inference can be based on a finite number of independent random
variables. It is shown that inference does not necessarily require  
simulation
of random measures. Rather, classical numerical integration can be  
used in the
most general cases.


http://front.math.ucdavis.edu/math.ST/0503055

---------------------------------------------------------------

3259. MODIFIED LOGARITHMIC SOBOLEV INEQUALITIES IN NULL CURVATURE

Ivan Gentil and  Arnaud Guillin and Laurent Miclo

We present a logarithmic Sobolev inequality adapted to a log-concave  
measure.
Assume that $\Phi$ is a symmetric convex function on $\dR$ satisfying
$(1+\e)\Phi(x)\leq {x}\Phi'(x)\leq(2-\e)\Phi(x)$ for $x\geq0$ large  
enough and
with $\e\in]0,1/2]$. We prove that the probability measure on $\dR$
$\mu_\Phi(dx)=e^{-\Phi(x)}/Z_\Phi dx$ satisfies a modified and adapted
logarithmic Sobolev inequality : there exist three constant $A,B,D>0$  
such that
for all smooth $f>0$, \begin{equation*}
   \ent{\mu_\Phi}{f^2}\leq A\int H_{\Phi}\PAR{{\frac{f'}{f}}}f^2d\mu_ 
\Phi,
\text{with} H_{\Phi}(x)= {\begin{array}{rl} \Phi^*\PAR{Bx} &\text{if
}\ABS{x}\geq D, x^2 &\text{if}\ABS{x}\leq D. \end{array} . \end 
{equation*}


http://front.math.ucdavis.edu/math.PR/0503585

---------------------------------------------------------------

3260. LENSES IN SKEW BROWNIAN FLOW

Krzysztof Burdzy and Haya Kaspi

We consider a stochastic flow in which individual particles follow skew
Brownian motions, with each one of these processes driven by the same  
Brownian
motion. One does not have uniqueness for the solutions of the  
corresponding
stochastic differential equation simultaneously for all real initial
conditions. Due to this lack of the simultaneous strong uniqueness  
for the
whole system of stochastic differential equations, the flow contains  
lenses,
that is, pairs of skew Brownian motions which start at the same point,
bifurcate, and then coalesce in a finite time. The paper contains  
qualitative
and quantitative (distributional) results on the geometry of the flow  
and
lenses.


http://front.math.ucdavis.edu/math.PR/0503586

---------------------------------------------------------------

3261. WEAK POINCARE INEQUALITIES ON DOMAINS DEFINED BY BROWNIAN ROUGH  
PATHS

Shigeki Aida

We prove weak Poincare inequalities on domains which are inverse  
images of
open sets in Wiener spaces under continuous functions of Brownian  
rough paths.
The result is applicable to Dirichlet forms on loop groups and  
connected open
subsets of path spaces over compact Riemannian manifolds.


http://front.math.ucdavis.edu/math.PR/0503587

---------------------------------------------------------------

3262. TIME CHANGES OF SYMMETRIC DIFFUSIONS AND FELLER MEASURES

Masatoshi Fukushima and  Ping He and Jiangang Ying

We extend the classical Douglas integral, which expresses the Dirichlet
integral of a harmonic function on the unit disk in terms of its  
value on
boundary, to the case of conservative symmetric diffusion in terms of  
Feller
measure, by using the approach of time change of Markov processes.


http://front.math.ucdavis.edu/math.PR/0503588

---------------------------------------------------------------

3263. DIFFERENCE PROPHET INEQUALITIES FOR [0,1]-VALUED I.I.D. RANDOM  
VARIABLES  WITH COST FOR OBSERVATIONS

Holger Kosters

Let X_1,X_2,... be a sequence of [0,1]-valued i.i.d. random  
variables, let
c\geq 0 be a sampling cost for each observation and let Y_i=X_i-ic,  
i=1,2,....
For n=1,2,..., let M(Y_1,...,Y_n)=E(max_{1\leq i\leq n}Y_i) and
V(Y_1,...,Y_n)=sup_{\tau \in C^n}E(Y_{\tau}), where C^n denotes the  
set of all
stopping rules for Y_1,...,Y_n. Sharp upper bounds for the difference
M(Y_1,...,Y_n)-V(Y_1,...,Y_n) are given under various restrictions on  
c and n.


http://front.math.ucdavis.edu/math.PR/0503589

---------------------------------------------------------------

3264. UNIQUENESS FOR DIFFUSIONS DEGENERATING AT THE BOUNDARY OF A  
SMOOTH  BOUNDED SET

Dante DeBlassie

For continuous \gamma, g:[0,1]\to(0,\infty), consider the degenerate
stochastic differential equation dX_t=[1-|X_t|^2]^{1/2}\gamma(|X_t|)
dB_t-g(|X_t|)X_t dt in the closed unit ball of R^n. We introduce a  
new idea to
show pathwise uniqueness holds when \gamma and g are Lipschitz and
\frac{g(1)}{\gamma^2(1)}>\sqrt2-1. When specialized to a case studied  
by Swart
[Stochastic Process. Appl. 98 (2002) 131-149] with \gamma=\sqrt2 and g 
\equiv c,
this gives an improvement of his result. Our method applies to more  
general
contexts as well. Let D be a bounded open set with C^3 boundary and  
suppose
h:\barD\to R Lipschitz on \barD, as well as C^2 on a neighborhood of  
\partial D
with Lipschitz second partials there. Also assume h>0 on D, h=0 on  
\partial D
and |\nabla h|>0 on \partial D. An example of such a function is
h(x)=d(x,\partial D). We give conditions which ensure pathwise  
uniqueness holds
for dX_t=h(X_t)^{1/2}\sigma(X_t) dB_t+b(X_t) dt in \barD.


http://front.math.ucdavis.edu/math.PR/0503590

---------------------------------------------------------------

3265. MODERATE DEVIATIONS FOR DIFFUSIONS WITH BROWNIAN POTENTIALS

Yueyun Hu and Zhan Shi

We present precise moderate deviation probabilities, in both quenched  
and
annealed settings, for a recurrent diffusion process with a Brownian  
potential.
Our method relies on fine tools in stochastic calculus, including  
Kotani's
lemma and Lamperti's representation for exponential functionals. In  
particular,
our result for quenched moderate deviations is in agreement with a  
recent
theorem of Comets and Popov [Probab. Theory Related Fields 126 (2003)  
571-609]
who studied the corresponding problem for Sinai's random walk in random
environment.


http://front.math.ucdavis.edu/math.PR/0503591

---------------------------------------------------------------

3266. SELF-INTERSECTION LOCAL TIME: CRITICAL EXPONENT, LARGE  
DEVIATIONS, AND  LAWS OF THE ITERATED LOGARITHM

Richard F. Bass and Xia Chen

If \beta_t is renormalized self-intersection local time for planar  
Brownian
motion, we characterize when Ee^{\gamma\beta_1} is finite or infinite  
in terms
of the best constant of a Gagliardo-Nirenberg inequality. We prove large
deviation estimates for \beta_1 and -\beta_1. We establish lim sup  
and lim inf
laws of the iterated logarithm for \beta_t as t\to\infty.


http://front.math.ucdavis.edu/math.PR/0503592

---------------------------------------------------------------

3267. EXPONENTIAL ASYMPTOTICS AND LAW OF THE ITERATED LOGARITHM FOR   
INTERSECTION LOCAL TIMES OF RANDOM WALKS

Xia Chen

Let \alpha ([0,1]^p) denote the intersection local time of p independent
d-dimensional Brownian motions running up to the time 1. Under the  
conditions
p(d-2)<d and d\ge 2, we prove lim_{t\to\infty}t^{-1}\log
P\bigl{\alpha([0,1]^p)\ge t^{(d(p-1))/2}\bigr}=-\gamma_{\alpha}(d,p)  
with the
right-hand side being identified in terms of the the best constant of  
the
Gagliardo-Nirenberg inequality. Within the scale of moderate  
deviations, we
also establish the precise tail asymptotics for the intersection  
local time
I_n=#{(k_1,...,k_p)\in [1,n]^p;S_1(k_1)=... =S_p(k_p)} run by the  
independent,
symmetric, Z^d-valued random walks S_1(n),...,S_p(n). Our results  
apply to the
law of the iterated logarithm. Our approach is based on Feynman-Kac  
type large
deviation, time exponentiation, moment computation and some  
technologies along
the lines of probability in Banach space. As an interesting  
coproduct, we
obtain the inequality \bigl(EI_{n_1+... +n_a}^m\bigr)^{1/p}\le \sum_ 
{k_1+...
+k_a=m\limits_{k_1,...,k_a\ge 0}}\frac{m!}{k_1!...
k_a!}\bigl(EI_{n_1}^{k_1}\bigr)^{1/p}... \bigl(EI_{n_a}^{k_a}\bigr)^ 
{1/p} in
the case of random walks.


http://front.math.ucdavis.edu/math.PR/0503593

---------------------------------------------------------------

3268. REGULARITY OF SOLUTIONS TO STOCHASTIC VOLTERRA EQUATIONS WITH  
INFINITE  DELAY

Anna Karczewska and  Carlos Lizama

The paper gives necessary and sufficient conditions providing  
regularity of
solutions to stochastic Volterra equations with infinite delay on a
$d$-dimensional torus. The harmonic analysis techniques and stochastic
integration in function spaces are used.


http://front.math.ucdavis.edu/math.PR/0503595

---------------------------------------------------------------

3269. A CLASS OF GENERALIZED HYPERBOLIC CONTINUOUS TIME INTEGRATED  
STOCHASTIC  VOLATILITY LIKELIHOOD MODELS

Lancelot F. James and John W. Lau

This paper discusses and analyzes a class of likelihood models which are
based on two distributional innovations in financial models for stock  
returns.
That is, the notion that the marginal distribution of aggregate  
returns of
log-stock prices are well approximated by generalized hyperbolic  
distributions,
and that volatility clustering can be handled by specifying the  
integrated
volatility as a random process such as that proposed in a recent  
series of
papers by Barndorff-Nielsen and Shephard (BNS). The BNS models produce
likelihoods for aggregate returns which can be viewed as a subclass  
of latent
regression models where one has n conditionally independent Normal  
random
variables whose mean and variance are representable as linear  
functionals of a
common unobserved Poisson random measure. James (2005b) recently  
obtains an
exact analysis for such models yielding expressions of the likelihood  
in terms
of quite tractable Fourier-Cosine integrals. Here, our idea is to  
analyze a
class of likelihoods, which can be used for similar purposes, but  
where the
latent regression models are based on n conditionally independent  
models with
distributions belonging to a subclass of the generalized hyperbolic
distributions and whose corresponding parameters are representable as  
linear
functionals of a common unobserved Poisson random measure. Our models  
are
perhaps most closely related to the Normal inverse Gaussian/GARCH/A- 
PARCH
models of Brandorff-Nielsen (1997) and Jensen and Lunde (2001), where  
in our
case the GARCH component is replaced by quantities such as INT-OU  
processes. It
is seen that, importantly, such likelihood models exhibit quite  
different
features structurally. One nice feature of the model is that it  
allows for more
flexibility in terms of modelling of external regression parameters.


http://front.math.ucdavis.edu/math.ST/0503056

---------------------------------------------------------------

3270. A LOCAL LIMIT THEOREM FOR DIRECTED POLYMERS IN RANDOM MEDIA:  
THE  CONTINUOUS AND THE DISCRETE CASE

Vincent Vargas (PMA)

In this article, we consider two models of directed polymers in random
environment: a discrete model and a continuous model. We consider  
these models
in dimension greater or equal to 3 and we suppose that the normalized  
partition
function is bounded in L^2. Under these assumptions, Sinai proved a  
local limit
theorem for the discrete model, using a perturbation expansion. In this
article, we give a new method for proving Sinai's local limit  
theorem. This new
method can be transposed to the continuous setting in which we prove  
a similar
local limit theorem.


http://front.math.ucdavis.edu/math.PR/0503596

---------------------------------------------------------------

3271. GLOBAL L_2-SOLUTIONS OF STOCHASTIC NAVIER-STOKES EQUATIONS

R. Mikulevicius and B. L. Rozovskii

This paper concerns the Cauchy problem in R^d for the stochastic
Navier-Stokes equation \partial_tu=\Delta u-(u,\nabla)u-\nabla p+f(u)+
[(\sigma,\nabla)u-\nabla \tilde p+g(u)]\circ \dot W, u(0)=u_0,\qquad  
divu=0,
driven by white noise \dot W. Under minimal assumptions on regularity  
of the
coefficients and random forces, the existence of a global weak  
(martingale)
solution of the stochastic Navier-Stokes equation is proved. In the
two-dimensional case, the existence and pathwise uniqueness of a  
global strong
solution is shown. A Wiener chaos-based criterion for the existence and
uniqueness of a strong global solution of the Navier-Stokes equations is
established.


http://front.math.ucdavis.edu/math.PR/0503597

---------------------------------------------------------------

3272. CENTRAL LIMIT THEOREMS FOR SEQUENCES OF MULTIPLE STOCHASTIC  
INTEGRALS

David Nualart and Giovanni Peccati

We characterize the convergence in distribution to a standard normal  
law for
a sequence of multiple stochastic integrals of a fixed order with  
variance
converging to 1. Some applications are given, in particular to study the
limiting behavior of quadratic functionals of Gaussian processes.


http://front.math.ucdavis.edu/math.PR/0503598

---------------------------------------------------------------

3273. STOCHASTIC INTEGRAL REPRESENTATION AND REGULARITY OF THE  
DENSITY FOR THE  EXIT MEASURE OF SUPER-BROWNIAN MOTION

Jean-Francois Le Gall and Leonid Mytnik

This paper studies the regularity properties of the density of the exit
measure for super-Brownian motion with (1+\beta)-stable branching  
mechanism. It
establishes the continuity of the density in dimension d=2 and the
unboundedness of the density in all other dimensions where the  
density exists.
An alternative description of the exit measure and its density is  
also given
via a stochastic integral representation. Results are applied to the
probabilistic representation of nonnegative solutions of the partial
differential equation \Delta u=u^{1+\beta}.


http://front.math.ucdavis.edu/math.PR/0503599

---------------------------------------------------------------

3274. PRECISE ASYMPTOTICS OF SMALL EIGENVALUES OF REVERSIBLE  
DIFFUSIONS IN THE  METASTABLE REGIME

Michael Eckhoff

We investigate the close connection between metastability of the  
reversible
diffusion process X defined by the stochastic differential equation
dX_t=-\nabla F(X_t) dt+\sqrt2\epsilon dW_t,\qquad \epsilon >0, and  
the spectrum
near zero of its generator -L_{\epsilon}\equiv \epsilon \Delta -\nabla
F\cdot\nabla, where F:R^d\to R and W denotes Brownian motion on R^d. For
generic F to each local minimum of F there corresponds a metastable  
state. We
prove that the distribution of its rescaled relaxation time converges  
to the
exponential distribution as \epsilon \downarrow 0 with optimal and  
uniform
error estimates. Each metastable state can be viewed as an eigenstate of
L_{\epsilon} with eigenvalue which converges to zero exponentially  
fast in
1/\epsilon. Modulo errors of exponentially small order in 1/\epsilon  
this
eigenvalue is given as the inverse of the expected metastable  
relaxation time.
The eigenstate is highly concentrated in the basin of attraction of the
corresponding trap.


http://front.math.ucdavis.edu/math.PR/0503600

---------------------------------------------------------------

3275. ASYMPTOTIC EXPANSIONS FOR THE LAPLACE APPROXIMATIONS OF SUMS OF  
BANACH  SPACE-VALUED RANDOM VARIABLES

Sergio Albeverio and Song Liang

Let X_i, i\in N, be i.i.d. B-valued random variables, where B is a real
separable Banach space. Let \Phi be a smooth enough mapping from B  
into R. An
asymptotic evaluation of Z_n=E(\exp (n\Phi (\sum_{i=1}^nX_i/n))), up  
to a
factor (1+o(1)), has been gotten in Bolthausen [Probab. Theory  
Related Fields
72 (1986) 305-318] and Kusuoka and Liang [Probab. Theory Related  
Fields 116
(2000) 221-238]. In this paper, a detailed asymptotic expansion of  
Z_n as n\to
\infty is given, valid to all orders, and with control on remainders.  
The
results are new even in finite dimensions.


http://front.math.ucdavis.edu/math.PR/0503601

---------------------------------------------------------------

3276. MULTIPLICATIVE MONOTONE CONVOLUTIONS

Uwe Franz

Recently, Bercovici has introduced multiplicative convolutions based on
Muraki's monotone independence and shown that these convolution of  
probability
measures correspond to the composition of some function of their Cauchy
transforms. We provide a new proof of this fact based on the  
combinatorics of
moments. We also give a new characterisation of the probability  
measures that
can be embedded into continuous monotone convolution semigroups of  
probability
measures on the unit circle and briefly discuss a relation to Galton- 
Watson
processes.


http://front.math.ucdavis.edu/math.PR/0503602

---------------------------------------------------------------

3277. EXTREMES ON TREES

Tailen Hsing and Holger Rootzen

This paper considers the asymptotic distribution of the longest edge  
of the
minimal spanning tree and nearest neighbor graph on X_1,...,X_{N_n}  
where
X_1,X_2,... are i.i.d. in \Re^2 with distribution F and N_n is  
independent of
the X_i and satisfies N_n/n\to_p1. A new approach based on spatial  
blocking and
a locally orthogonal coordinate system is developed to treat cases  
for which F
has unbounded support. The general results are applied to a number of  
special
cases, including elliptically contoured distributions, distributions  
with
independent Weibull-like margins and distributions with parallel  
level curves.


http://front.math.ucdavis.edu/math.PR/0503603

---------------------------------------------------------------

3278. ON THE MONOTONICITY OF THE SPEED OF RANDOM WALKS ON A  
PERCOLATION  CLUSTER OF TREES

Dayue Chen and Fuxi Zhang

We consider the simple random walk on the infinite cluster of the  
Bernoulli
bond percolation of trees, and investigate the relation between the  
speed of
the simple random walk and the retaining probability $p$ by studying  
three
classes of trees. A sufficient condition is established for Galton- 
Watson
trees.


http://front.math.ucdavis.edu/math.PR/0503610

---------------------------------------------------------------

3279. CONTRACTIVE MARKOV SYSTEMS II

Ivan Werner

In this paper, we continue development of the theory of contractive  
Markov
systems (CMSs) initiated in \cite{Wer1}. We extend some results from
\cite{Wer1}, \cite{Wer3}, \cite{Wer5} and \cite{Wer6} to the case of
contractive Markov systems with probabilities which have a square  
summable
variation by using some ideas of A. Johansson and A. Oeberg \cite 
{JO}. In
particular, we show that an irreducible CMS has a unique invariant Borel
probability measure if the vertex sets form an open partition of the  
state
space and the restrictions of the probability functions on their  
vertex sets
have a square summable variation and are bounded away from zero.


http://front.math.ucdavis.edu/math.PR/0503633

---------------------------------------------------------------

3280. LIMIT THEOREMS FOR ITERATED RANDOM TOPICAL OPERATORS

Glenn Merlet (IRMAR)

Let A(n) be a sequence of i.i.d. topical (i.e. isotone and additively
homogeneous) operators. Let $x(n,x\_0)$ be defined by $x(0,x\_0)=x\_0 
$ and
$x(n,x\_0)=A(n)x(n-1,x\_0)$. This can modelize a wide range of systems
including, task graphs, train networks, Job-Shop, timed digital  
circuits or
parallel processing systems. When A(n) has the memory loss property,  
we use the
spectral gap method to prove limit theorems for $x(n,x\_0)$. Roughly  
speaking,
we show that $x(n,x\_0)$ behaves like a sum of i.i.d. real variables.
Precisely, we show that with suitable additional conditions, it  
satisfies a
central limit theorem with rate, a local limit theorem, a renewal  
theorem and a
large deviations principle, and we give an algebraic condition to  
ensure the
positivity of the variance in the CLT. When A(n) are defined by  
matrices in the
\mp semi-ring, we give more effective statements and show that the  
additional
conditions and the positivity of the variance in the CLT are generic.


http://front.math.ucdavis.edu/math.PR/0503634

---------------------------------------------------------------

3281. A PROBABILISTIC APPROACH TO THE GEOMETRY OF THE \ELL_P^N-BALL

Franck Barthe and  Olivier Guedon and  Shahar Mendelson and Assaf Naor

This article investigates, by probabilistic methods, various geometric
questions on B_p^n, the unit ball of \ell_p^n. We propose  
realizations in terms
of independent random variables of several distributions on B_p^n,  
including
the normalized volume measure. These representations allow us to  
unify and
extend the known results of the sub-independence of coordinate slabs  
in B_p^n.
As another application, we compute moments of linear functionals on  
B_p^n,
which gives sharp constants in Khinchine's inequalities on B_p^n and  
determines
the \psi_2-constant of all directions on B_p^n. We also study the  
extremal
values of several Gaussian averages on sections of B_p^n (including  
mean width
and \ell-norm), and derive several monotonicity results as p varies.
Applications to balancing vectors in \ell_2 and to covering numbers of
polyhedra complete the exposition.


http://front.math.ucdavis.edu/math.PR/0503650

---------------------------------------------------------------

3282. MOMENT INEQUALITIES FOR FUNCTIONS OF INDEPENDENT RANDOM VARIABLES

Stephane Boucheron and  Olivier Bousquet and  Gabor Lugosi and Pascal  
Massart

A general method for obtaining moment inequalities for functions of
independent random variables is presented. It is a generalization of the
entropy method which has been used to derive concentration  
inequalities for
such functions [Boucheron, Lugosi and Massart Ann. Probab. 31 (2003)
1583-1614], and is based on a generalized tensorization inequality  
due to
Latala and Oleszkiewicz [Lecture Notes in Math. 1745 (2000) 147-168].  
The new
inequalities prove to be a versatile tool in a wide range of  
applications. We
illustrate the power of the method by showing how it can be used to
effortlessly re-derive classical inequalities including Rosenthal and
Kahane-Khinchine-type inequalities for sums of independent random  
variables,
moment inequalities for suprema of empirical processes and moment  
inequalities
for Rademacher chaos and U-statistics. Some of these corollaries are  
apparently
new. In particular, we generalize Talagrand's exponential inequality for
Rademacher chaos of order 2 to any order. We also discuss  
applications for
other complex functions of independent random variables, such as  
suprema of
Boolean polynomials which include, as special cases, subgraph  
counting problems
in random graphs.


http://front.math.ucdavis.edu/math.PR/0503651

---------------------------------------------------------------

3283. ON THE STOCHASTIC CALCULUS METHOD FOR SPINS SYSTEMS

Samy Tindel

In this note we show how to generalize the stochastic calculus method
introduced by Comets and Neveu [Comm. Math. Phys. 166 (1995) 549-564]  
for two
models of spin glasses, namely, the SK model with external field and the
perceptron model. This method allows to derive quite easily some  
fluctuation
results for the free energy in those two cases.


http://front.math.ucdavis.edu/math.PR/0503652

---------------------------------------------------------------

3284. CLOSURES OF EXPONENTIAL FAMILIES

Imre Csiszar and Frantisek Matus

The variation distance closure of an exponential family with a convex  
set of
canonical parameters is described, assuming no regularity conditions.  
The tools
are the concepts of convex core of a measure and extension of an  
exponential
family, introduced previously by the authors, and a new concept of  
accessible
faces of a convex set. Two other closures related to the information  
divergence
are also characterized.


http://front.math.ucdavis.edu/math.PR/0503653

---------------------------------------------------------------

3285. ONE-DEPENDENT TRIGONOMETRIC DETERMINANTAL PROCESSES ARE  TWO- 
BLOCK-FACTORS

Erik I. Broman

Given a trigonometric polynomial f:[0,1]\to[0,1] of degree m, one can  
define
a corresponding stationary process {X_i}_{i\in Z} via determinants of  
the
Toeplitz matrix for f. We show that for m=1 this process, which is  
trivially
one-dependent, is a two-block-factor.


http://front.math.ucdavis.edu/math.PR/0503654

---------------------------------------------------------------

3286. ASYMPTOTICS FOR HITTING TIMES

M. Kupsa and Y. Lacroix

In this paper we characterize possible asymptotics for hitting times in
aperiodic ergodic dynamical systems: asymptotics are proved to be the
distribution functions of subprobability measures on the line  
belonging to the
functional class {6pt} {-3mm}(A){6mm}F={F:R\to [0,1]:\left\lbrack  
\matrixF is
increasing, null on ]-\infty, 0]; \noalignF is continuous and concave;
\noalignF(t)\le t for t\ge 0.\right.}. {6pt} Note that all possible  
asymptotics
are absolutely continuous.


http://front.math.ucdavis.edu/math.PR/0503655

---------------------------------------------------------------

3287. KREIN'S SPECTRAL THEORY AND THE PALEY-WIENER EXPANSION FOR  
FRACTIONAL  BROWNIAN MOTION

Kacha Dzhaparidze and Harry van Zanten

In this paper we develop the spectral theory of the fractional Brownian
motion (fBm) using the ideas of Krein's work on continuous analogous of
orthogonal polynomials on the unit circle. We exhibit the functions  
which are
orthogonal with respect to the spectral measure of the fBm and obtain an
explicit reproducing kernel in the frequency domain. We use these  
results to
derive an extension of the classical Paley-Wiener expansion of the  
ordinary
Brownian motion to the fractional case.


http://front.math.ucdavis.edu/math.PR/0503656

---------------------------------------------------------------

3288. CRITICALITY FOR BRANCHING PROCESSES IN RANDOM ENVIRONMENT

V. I. Afanasyev and  J. Geiger and  G. Kersting and V. A. Vatutin

We study branching processes in an i.i.d. random environment, where the
associated random walk is of the oscillating type. This class of  
processes
generalizes the classical notion of criticality. The main properties  
of such
branching processes are developed under a general assumption, known as
Spitzer's condition in fluctuation theory of random walks, and some  
additional
moment condition. We determine the exact asymptotic behavior of the  
survival
probability and prove conditional functional limit theorems for the  
generation
size process and the associated random walk. The results rely on a  
stimulating
interplay between branching process theory and fluctuation theory of  
random
walks.


http://front.math.ucdavis.edu/math.PR/0503657

---------------------------------------------------------------

3289. EXAMPLES OF MODERATE DEVIATION PRINCIPLE FOR DIFFUSION PROCESSES

A. Guillin} and  R. Liptser

Taking into account some likeness of moderate deviations (MD) and  
central
limit theorems (CLT), we develop an approach, which made a good  
showing in CLT,
for MD analysis of a family $$ S^\kappa_t=\frac{1}{t^\kappa}\int_0^tH 
(X_s)ds, \
t\to\infty $$ for an ergodic diffusion process $X_t$ under $0.5< 
\kappa<1$ and
appropriate $H$. We mean a decomposition with ``corrector'': $$
\frac{1}{t^\kappa}\int_0^tH(X_s)ds={\rm
corrector}+\frac{1}{t^\kappa}\underbrace{M_t}_{\rm martingale}. $$  
and show
that, as in the CLT analysis, the corrector is negligible but in the  
MD scale,
and the main contribution in the MD brings the family ``$
\frac{1}{t^\kappa}M_t, t\to\infty. $'' Starting from Bayer and Freidlin,
\cite{BF}, and finishing by Wu's papers \cite{Wu1}-\cite{WuH}, in the  
MD study
Laplace's transform dominates. In the paper, we replace the Laplace  
technique
by one, admitting to give the conditions, providing the MD, in terms of
``drift-diffusion'' parameters and $H$. However, a verification of these
conditions heavily depends on a specificity of a diffusion model.  
That is why
the paper is named ``Examples ...''.


http://front.math.ucdavis.edu/math.PR/0503070

---------------------------------------------------------------

3290. CONFIDENCE INTERVALS FOR NONHOMOGENEOUS BRANCHING PROCESSES  
AND  POLYMERASE CHAIN REACTIONS

Didier Piau

We extend in two directions our previous results about the sampling  
and the
empirical measures of immortal branching Markov processes. Direct  
applications
to molecular biology are rigorous estimates of the mutation rates of  
polymerase
chain reactions from uniform samples of the population after the  
reaction.
First, we consider nonhomogeneous processes, which are more adapted  
to real
reactions. Second, recalling that the first moment estimator is  
analytically
known only in the infinite population limit, we provide rigorous  
confidence
intervals for this estimator that are valid for any finite  
population. Our
bounds are explicit, nonasymptotic and valid for a wide class of  
nonhomogeneous
branching Markov processes that we describe in detail. In the setting of
polymerase chain reactions, our results imply that enlarging the size  
of the
sample becomes useless for surprisingly small sizes. Establishing  
confidence
intervals requires precise estimates of the second moment of random  
samples.
The proof of these estimates is more involved than the proofs that  
allowed us,
in a previous paper, to deal with the first moment. On the other  
hand, our
method uses various, seemingly new, monotonicity properties of the  
harmonic
moments of sums of exchangeable random variables.


http://front.math.ucdavis.edu/math.PR/0503659

---------------------------------------------------------------

3291. SECTORIAL CONVERGENCE OF U-STATISTICS

Anda Gadidov

In this note we show that almost sure convergence to zero of symmetrized
U-statistics indexed by a linear sector in Z^d_+ is equivalent to  
convergence
along the diagonal of Z^d_+, as it is considered in Lata\la and Zinn  
[Ann.
Probab. 28 (2000) 1908-1924]. Comparisons with similar results for  
sums of
multi-indexed i.i.d. random variables are also made.


http://front.math.ucdavis.edu/math.PR/0503660

---------------------------------------------------------------

3292. A STRONG INVARIANCE PRINCIPLE FOR ASSOCIATED RANDOM FIELDS

Raluca M. Balan

In this paper we generalize Yu's [Ann. Probab. 24 (1996) 2079-2097]  
strong
invariance principle for associated sequences to the multi-parameter  
case,
under the assumption that the covariance coefficient u(n) decays  
exponentially
as n\to \infty. The main tools that we use are the following: the  
Berkes and
Morrow [Z. Wahrsch. Verw. Gebiete 57 (1981) 15-37] multi-parameter  
blocking
technique, the Csorgo and Revesz [Z. Wahrsch. Verw. Gebiete 31 (1975)  
255-260]
quantile transform method and the Bulinski [Theory Probab. Appl. 40  
(1995)
136-144] rate of convergence in the CLT.


http://front.math.ucdavis.edu/math.PR/0503661

---------------------------------------------------------------

3293. MODERATE DEVIATION PRINCIPLE FOR ERGODIC MARKOV CHAIN.  
LIPSCHITZ  SUMMANDS

B. Delyon and  A. Juditsky and  R. Liptser

For ${1/2}<\alpha<1$, we propose the MDP analysis for family $$
S^\alpha_n=\frac{1}{n^\alpha}\sum_{i=1}^nH(X_{i-1}), n\ge 1, $$ where
$(X_n)_{n\ge 0}$ be a homogeneous ergodic Markov chain, $X_n\in  
\mathbb{R}^d$,
when the spectrum of operator $P_x$ is continuous. The vector-valued  
function
$H$ is not assumed to be bounded but the Lipschitz continuity of $H$ is
required. The main helpful tools in our approach are Poisson's  
equation and
Stochastic Exponential; the first enables to replace the original  
family by
$\frac{1}{n^\alpha}M_n$ with a martingale $M_n$ while the second to  
avoid the
direct Laplace transform analysis.


http://front.math.ucdavis.edu/math.PR/0503071

---------------------------------------------------------------

3294. DISTANCES IN RANDOM GRAPHS WITH FINITE MEAN AND INFINITE  
VARIANCE  DEGREES

Remco van der Hofstad and  Gerard Hooghiemstra and  Dmitri Znamenski

In this paper we study random graphs with independent and identically
distributed degrees of which the tail of the distribution function is  
regularly
varying with exponent $\tau\in (2,3)$.
   The number of edges between two arbitrary nodes, also called the  
graph
distance or hopcount, in a graph with $N$ nodes is investigated when  
$N\to
\infty$. When $\tau\in (2,3)$, this graph distance grows like $2\frac 
{\log\log
N}{|\log(\tau-2)|}$. In different papers, the cases $\tau>3$ and $\tau 
\in
(1,2)$ have been studied. We also study the fluctuations around these
asymptotic means, and describe their distributions. The results  
presented here
improve upon results of Reittu and Norros, who prove an upper bound  
only.


http://front.math.ucdavis.edu/math.PR/0502581

---------------------------------------------------------------

3295. ON TAIL DISTRIBUTIONS OF SUPREMUM AND QUADRATIC VARIATION OF  
LOCAL  MARTINGALES

R. Liptser and  A. Novikov

We extend some known results relating the distribution tails of a  
continuous
local martingale supremum and its quadratic variation to the case of  
locally
square integrable martingales with bounded jumps. The predictable and  
optional
quadratic variations are involved in the main result.


http://front.math.ucdavis.edu/math.PR/0503072

---------------------------------------------------------------

3296. LIMIT THEOREMS FOR BIPOWER VARIATION IN FINANCIAL ECONOMETRICS

Ole E. Barndorff-Nielsen (DEPT Math Sci) and  Svend E. Graversen  
(DEPT  Math Sci), Jean Jacod (PMA), Neil Shephard (NUFFIELD College)

In this paper we provide an asymptotic analysis of generalised bipower
measures of the variation of price processes in financial economics.  
These
measures encompass the usual quadratic variation, power variation and  
bipower
variations which have been highlighted in recent years in financial
econometrics. The analysis is carried out under some rather general  
Brownian
semimartingale assumptions, which allow for standard leverage effects.


http://front.math.ucdavis.edu/math.PR/0503711

---------------------------------------------------------------

3297. RANDOM WALKS IN A DIRICHLET ENVIRONMENT

Nathana\"el Enriquez and  Christophe Sabot

This paper states a law of large numbers for a random walk in a  
random iid
environment on ${\mathbb Z}^d$, where the environment follows some  
Dirichlet
distribution. Moreover, we give explicit bounds for the asymptotic  
velocity of
the process and also an asymptotic expansion of this velocity at low  
disorder.


http://front.math.ucdavis.edu/math.PR/0503713

---------------------------------------------------------------

3298. RANDOM WALKS IN A RANDOM ENVIRONMENT

S R S Varadhan

Random walks as well as diffusions in random media are considered.  
Methods
are developed that allow one to establish large deviation results for  
both the
`quenched' and the `averaged' case.


http://front.math.ucdavis.edu/math.PR/0503089

---------------------------------------------------------------

3299. RANDOM TREES AND GENERAL BRANCHING PROCESSES

Anna Rudas and  Balint Toth and  Benedek Valko

We consider a model of random tree growth, where at each time unit a new
vertex is added and attached to an already existing vertex chosen at  
random.
The probability with which a vertex with degree $k$ is chosen is  
proportional
to $w(k)$, where the weight function $w$ is the parameter of the model.
   In the papers of B. Bollobas, O. Riordan, J. Spencer, G. Tusnady,  
and,
independently, Mori, the asymptotic degree distribution is obtained  
for a model
that is equivalent to the special case of ours, when the weight  
function is
linear. The proof therein strongly relies on the linear choice of $w$.
   We give the asymptotical degree distribution for a wide range of  
weight
functions. Moreover, we provide the asymptotic distribution of the  
tree itself
as seen from a randomly selected vertex. The latter approach is new  
and gives
full insight to the limiting structure of the tree.
   Our proof relies on the fact that considering the evolution of the  
random
tree in continuous time, the process may be viewed as a general  
branching
process, this way classical results can be applied.


http://front.math.ucdavis.edu/math.PR/0503728

---------------------------------------------------------------

3300. MIXED POISSON APPROXIMATION OF NODE DEPTH DISTRIBUTIONS IN  
RANDOM BINARY  SEARCH TREES

Rudolf Grubel and Nikolce Stefanoski

We investigate the distribution of the depth of a node containing a  
specific
key or, equivalently, the number of steps needed to retrieve an item  
stored in
a randomly grown binary search tree. Using a representation in terms  
of mixed
and compounded standard distributions, we derive approximations by  
Poisson and
mixed Poisson distributions; these lead to asymptotic normality  
results. We are
particularly interested in the influence of the key value on the  
distribution
of the node depth. Methodologically our message is that the explicit
representation may provide additional insight if compared to the  
standard
approach that is based on the recursive structure of the trees.  
Further, in
order to exhibit the influence of the key on the distributional  
asymptotics, a
suitable choice of distance of probability distributions is  
important. Our
results are also applicable in connection with the number of  
recursions needed
in Hoare's [Comm. ACM 4 (1961) 321-322] selection algorithm Find.


http://front.math.ucdavis.edu/math.PR/0503738

---------------------------------------------------------------

3301. ON FRACTIONAL TEMPERED STABLE MOTION

C. Houdr\'e and  R. Kawai

Fractional tempered stable motion (fTSm)} is defined and studied.  
FTSm has
the same covariance structure as fractional Brownian motion, while  
having tails
heavier than Gaussian but lighter than stable. Moreover, in short  
time it is
close to fractional stable L\'evy motion, while it is approximately  
fractional
Brownian motion in long time. A series representation of fTSm is  
derived and
used for simulation and to study some of its sample path properties.


http://front.math.ucdavis.edu/math.PR/0503741

---------------------------------------------------------------

3302. ON LAYERED STABLE PROCESSES

C. Houdr\'e and  R. Kawai

Layered stable (multivariate) distributions and processes are defined  
and
studied. A layered stable process combines stable trends of two  
different
indices, one of them possibly Gaussian. More precisely, in short  
time, it is
close to a stable process while, in long time, it approximates  
another stable
(possibly Gaussian) process. We also investigate the absolute  
continuity of a
layered stable process with respect to its short time limiting stable  
process.
A series representation of layered stable processes is derived,  
giving insights
into both the structure of the sample paths and of the short and long  
time
behaviors. This series is further used for sample paths simulation.


http://front.math.ucdavis.edu/math.PR/0503742

---------------------------------------------------------------

3303. MEASURE FREE MARTINGALES

Rajeeva L Karandikar and M G Nadkarni

We give a necessary and sufficient condition on a sequence of  
functions on a
set $\Omega$ under which there is a measure on $\Omega$ which renders  
the given
sequence of functions a martingale. Further such a measure is unique  
if we
impose a natural maximum entropy condition on the conditional  
probabilities.


http://front.math.ucdavis.edu/math.PR/0503099

---------------------------------------------------------------

3304. METRIC STABILITY FOR RANDOM WALKS (WITH APPLICATIONS IN  
RENORMALIZATION  THEORY)

Carlos G. Moreira (IMPA-Brazil) Daniel Smania (ICMC-USP-Brazil)

Consider deterministic random walks F: I x Z -> I x Z, defined by
F(x,n)=(f(x), K(x)+n), where f is an expanding Markov map on the  
interval I and
K: I->Z. We study the universality (stability) of ergodic (for instance,
recurrence and transience), geometric and multifractal properties in  
the class
of perturbations of the type G(x,n)=(f_n(x), L(x,n)+n) which are  
topologically
conjugate with F and f_n are expanding maps exponentially close to f  
when |n|
goes to infinity. We give applications of these results in the study  
of the
regularity of conjugacies between (generalized) infinitely  
renormalizable maps
of the interval and the existence of wild attractors for one- 
dimensional maps.


http://front.math.ucdavis.edu/math.DS/0503736

---------------------------------------------------------------

3305. THE JAMMED PHASE OF THE BIHAM-MIDDLETON-LEVINE TRAFFIC MODEL

Omer Angel and  Alexander E Holroyd and James B Martin

Initially a car is placed with probability p at each site of the
two-dimensional integer lattice. Each car is equally likely to be  
East-facing
or North-facing, and different sites receive independent assignments.  
At odd
time steps, each North-facing car moves one unit North if there is a  
vacant
site for it to move into. At even time steps, East-facing cars move  
East in the
same way. We prove that when p is sufficiently close to 1 traffic is  
jammed, in
the sense that no car moves infinitely many times. The result extends to
several variant settings, including a model with cars moving at  
random times,
and higher dimensions.


http://front.math.ucdavis.edu/math.PR/0504001

---------------------------------------------------------------

3306. BSDE WITH QUADRATIC GROWTH AND UNBOUNDED TERMINAL VALUE

Philippe Briand (IRMAR) and  Ying Hu (IRMAR)

In this paper, we study the existence of solution to BSDE with quadratic
growth and unbounded terminal value. We apply a localization  
procedure together
with a priori bounds. As a byproduct, we apply the same method to  
extend a
result on BSDEs with integrable terminal condition.


http://front.math.ucdavis.edu/math.PR/0504002

---------------------------------------------------------------

3307. THE HEAT EQUATION WITH MULTIPLICATIVE STABLE L\'EVY NOISE

Carl Mueller and Leonid Mytnik and Aurel Stan

We study the heat equation with a random potential term. The  
potential is a
one-sided stable noise, with positive jumps, which does not depend on  
time. To
avoid singularities, we define the equation in terms of a  
construction similar
to the Skorokhod integral or Wick product. We give a criterion for  
existence
based on the dimension of the space variable, and the parameter p of  
the stable
noise. Our arguments are different for p<1 and p>1.


http://front.math.ucdavis.edu/math.PR/0504027

---------------------------------------------------------------

3308. THE FULL SCALING LIMIT OF TWO-DIMENSIONAL CRITICAL PERCOLATION

Federico Camia and  Charles M. Newman

We use SLE(6) paths to construct a process of continuum nonsimple  
loops in
the plane and prove that this process coincides with the full  
continuum scaling
limit of 2D critical site percolation on the triangular lattice --  
that is, the
scaling limit of the set of all interfaces between different  
clusters. Some
properties of the loop process, including conformal invariance, are also
proved. In the main body of the paper these results are proved while  
assuming,
as argued by Schramm and Smirnov, that the percolation exploration path
converges in distribution to the trace of chordal SLE(6). Then, in a  
lengthy
appendix, a detailed proof is provided for this convergence to SLE 
(6), which
itself relies on Smirnov's result that crossing probabilities  
converge to
Cardy's formula.


http://front.math.ucdavis.edu/math.PR/0504036

---------------------------------------------------------------

3309. MINIMAX AND ADAPTIVE ESTIMATION OF THE WIGNER FUNCTION IN  
QUANTUM  HOMODYNE TOMOGRAPHY WITH NOISY DATA

Cristina Butucea (PMA and  MODALX) and  Madalin Guta and  Luis Artiles

We estimate the quantum state of a light beam from results of quantum
homodyne measurements performed on identically prepared quantum  
systems. The
state is represented through the Wigner function, a density on R2  
which may
take negative values but must respect intrinsic positivity  
constraints imposed
by quantum physics. The effect of the losses due to detection  
inefficiencies
which are always present in a real experiment is the addition to the
tomographic data of independent Gaussian noise. We construct a kernel  
estimator
for the Wigner function and prove that it is minimax efficient for the
pointwise risk over a class of infinitely differentiable functions.  
For the L2
risk, we compute the upper bounds of a truncated kernel estimator  
over the same
classes, restricted to functions with sub-Gaussian asymptotic  
behaviour. We
construct adaptive estimators, i.e. which do not depend on the  
smoothness
parameters, and prove that in some set-ups they attain the minimax  
rates for
the corresponding smoothness class.


http://front.math.ucdavis.edu/math.PR/0504058

---------------------------------------------------------------

3310. POINT PROCESS MODEL OF 1/F NOISE VERSUS A SUM OF LORENTZIANS

B. Kaulakys and  V. Gontis and  and M. Alaburda

We present a simple point process model of $1/f^{\beta}$ noise, covering
different values of the exponent $\beta$. The signal of the model  
consists of
pulses or events. The interpulse, interevent, interarrival,  
recurrence or
waiting times of the signal are described by the general Langevin  
equation with
the multiplicative noise and stochastically diffuse in some interval  
resulting
in the power-law distribution. Our model is free from the requirement  
of a wide
distribution of relaxation times and from the power-law forms of the  
pulses. It
contains only one relaxation rate and yields $1/f^ {\beta}$ spectra  
in a wide
range of frequency. We obtain explicit expressions for the power  
spectra and
present numerical illustrations of the model. Further we analyze the  
relation
of the point process model of $1/f$ noise with the Bernamont-Surdin- 
McWhorter
model, representing the signals as a sum of the uncorrelated  
components. We
show that the point process model is complementary to the model based  
on the
sum of signals with a wide-range distribution of the relaxation  
times. In
contrast to the Gaussian distribution of the signal intensity of the  
sum of the
uncorrelated components, the point process exhibits asymptotically a  
power-law
distribution of the signal intensity. The developed multiplicative point
process model of $1/f^{\beta}$ noise may be used for modeling and  
analysis of
stochastic processes in different systems with the power-law  
distribution of
the intensity of pulsing signals.


http://front.math.ucdavis.edu/cond-mat/0504025

---------------------------------------------------------------

3311. A RANDOM WALK PROOF OF THE ERDOS-TAYLOR CONJECTURE

Jay Rosen

For the simple random walk in Z^2 we study those points which are  
visited an
unusually large number of times, and provide a new proof of the Erdos- 
Taylor
conjecture describing the number of visits to the most visited point.


http://front.math.ucdavis.edu/math.PR/0503108

---------------------------------------------------------------

3312. WHAT IS ALWAYS STABLE IN NONLINEAR FILTERING?

P. Chigansky and  R. Liptser

This note addresses certain stability properties of the nonlinear  
filtering
equation in discrete time. The available positive and negative  
results indicate
that much depends on the structure of the signal state space, its  
ergodic
properties and observations regularity. We show that certain predicting
estimates are stable under surprisingly general assumptions.


http://front.math.ucdavis.edu/math.PR/0504094

---------------------------------------------------------------

3313. HOW LIKELY IS AN I.I.D. DEGREE SEQUENCE TO BE GRAPHICAL?

Richard Arratia and Thomas M. Liggett

Given i.i.d. positive integer valued random variables D_1,...,D_n,  
one can
ask whether there is a simple graph on n vertices so that the degrees  
of the
vertices are D_1,...,D_n. We give sufficient conditions on the  
distribution of
D_i for the probability that this be the case to be asymptotically 0,  
{1/2} or
strictly between 0 and {1/2}. These conditions roughly correspond to  
whether
the limit of nP(D_i\geq n) is infinite, zero or strictly positive and  
finite.
This paper is motivated by the problem of modeling large communications
networks by random graphs.


http://front.math.ucdavis.edu/math.PR/0504096

---------------------------------------------------------------

3314. THE UNIVERSALITY CLASSES IN THE PARABOLIC ANDERSON MODEL

Remco van der Hofstad and  Wolfgang Koenig and  Peter Moerters

We discuss the long time behaviour of the parabolic Anderson model, the
Cauchy problem for the heat equation with random potential on $\Z^d$. We
consider general i.i.d. potentials and show that exactly \emph{four}
qualitatively different types of intermittent behaviour can occur.  
These four
universality classes depend on the upper tail of the potential  
distribution:
(1) tails at $\infty$ that are thicker than the double-exponential  
tails, (2)
double-exponential tails at $\infty$ studied by G\"artner and  
Molchanov, (3) a
new class called \emph{almost bounded potentials}, and (4) potentials  
bounded
from above studied by Biskup and K\"onig. The new class (3), which  
contains
both unbounded and bounded potentials, is studied in both the  
annealed and the
quenched setting. We show that intermittency occurs on unboundedly  
increasing
islands whose diameter is slowly varying in time. The characteristic
variational formulas describing the optimal profiles of the potential  
and of
the solution are solved explicitly by parabolas, respectively, Gaussian
densities.


http://front.math.ucdavis.edu/math.PR/0504102

---------------------------------------------------------------

3315. INVARIANCE PRINCIPLES FOR LABELED MOBILES AND BIPARTITE PLANAR  
MAPS

Jean-Fran\c{c}ois Marckert (LM-Versailles) and  Gr\'{e}gory Miermont   
(LM-Orsay)

A class of labeled trees, called mobiles, was introduced by Bouttier-di
Francesco and Guitter in order to generalize the bijective studies of  
planar
maps initiated by Cori-Vauquelin and Schaeffer. We prove an invariance
principle for rescaled random mobiles associated with bipartite  
random planar
maps under a Boltzmann distribution. We infer that the latter  
converge in a
certain sense to the Brownian map introduced by Marckert and  
Mokkadem, which
encompasses results of Chassaing and Schaeffer on quadrangulations  
(although in
a slightly different context). These results are derived from a new  
invariance
principle for a class of two-type Galton-Watson trees coupled with a  
spatial
motion, which are shown to converge to the Brownian snake.


http://front.math.ucdavis.edu/math.PR/0504110

---------------------------------------------------------------

3316. TRACY-WIDOM LIMIT FOR THE LARGEST EIGENVALUE OF A LARGE CLASS  
OF COMPLEX  WISHART MATRICES

Noureddine El Karoui

We study the limiting behavior of the largest eigenvalue of a large  
class of
complex Wishart matrices. In other words, let X be an n*p matrix, and  
let its
rows be i.i.d complex normal N_{C}(0,Sigma_p). We denote by H_p the  
spectral
distribution of Sigma_p, and call lambda_i's its ordered eigenvalues.  
Let us
call l_i's the ordered eigenvalues of X^*X and c the unique root in
[0,1/lambda_1(Sigma_p)) of the equation
   \int ((lambda c)/(1-\lambda c))^2 dH_p(lambda) = n/p. The main  
result of this
paper is that, under technical conditions on (Sigma_p,n,p), we have,  
when
n->\infty,
   (l_1(X^*X)-n mu)/(n^{1/3} sigma) -> TW_2 .
  We give explicit formulas for mu and sigma, that depend non  
trivially on c.
Here TW_2 denotes the Tracy-Widom law appearing in the study of the  
Gaussian
Unitary Ensemble.
   This theorem applies to a number of covariance models found in  
applications,
including well-behaved Toeplitz matrices and covariance matrices  
whose spectral
distribution is a sum of atoms (under some conditions on the mass of the
atoms). Generalizations of the theorem to certain spiked versions of  
models in
G and a.s statements about l_1/n are given. Most known examples of  
convergence
of the largest eigenvalue of a complex sample covariance matrix to this
Tracy-Widom law are subcases of this result.


http://front.math.ucdavis.edu/math.PR/0503109

---------------------------------------------------------------

3317. DETERMINANTAL PROCESSES AND INDEPENDENCE

J. Ben Hough and  Manjunath Krishnapur and  Yuval Peres and Balint Virag

We give a probabilistic introduction to determinantal and permanental  
point
processes. Determinantal processes arise in physics (fermions,  
eigenvalues of
random matrices) and in combinatorics (nonintersecting paths, random  
spanning
trees). They have the striking property that the number of points in  
a region
$D$ is a sum of independent Bernoulli random variables, with  
parameters which
are eigenvalues of the relevant operator on $L^2(D)$. Moreover, any
determinantal process can be represented as a mixture of determinantal
projection processes. We give a simple explanation for these known  
facts, and
establish analogous representations for permanental processes, with  
geometric
variables replacing the Bernoulli variables. These representations  
lead to
simple proofs of existence criteria and central limit theorems, and  
unify known
results on the distribution of absolute values in certain processes with
radially symmetric distributions.


http://front.math.ucdavis.edu/math.PR/0503110

---------------------------------------------------------------

3318. RANDOM WALK ON THE INCIPIENT INFINITE CLUSTER ON TREES

Martin T. Barlow and Takashi Kumagai

Let ${\cal G}$ be the incipient infinite cluster (IIC) for  
percolation on a
homogeneous tree of degree $n_0+1$. We obtain estimates for the  
transition
density of the continuous time simple random walk $Y$ on ${\cal G}$; the
process satisfies anomalous diffusion and has spectral dimension 4/3.


http://front.math.ucdavis.edu/math.PR/0503118

---------------------------------------------------------------

3319. QUANTITATIVE CONCENTRATION INEQUALITIES FOR EMPIRICAL MEASURES  
ON  NON-COMPACT SPACES

Francois Bolley and  Arnaud Guillin and  Cedric Villani

We establish some quantitative concentration estimates for the empirical
measure of many independent variables, in transportation distances.  
As an
application, we provide some error bounds for particle simulations in  
a model
mean field problem. The tools include coupling arguments, as well as  
regularity
and moments estimates for solutions of certain diffusive partial  
differential
equations.


http://front.math.ucdavis.edu/math.PR/0503123

---------------------------------------------------------------

3320. ON THE BIAS OF TRACEROUTE SAMPLING; OR, POWER-LAW DEGREE  
DISTRIBUTIONS  IN REGULAR GRAPHS

Dimitris Achlioptas and  Aaron Clauset and  David Kempe and  and  
Cristopher Moore

Understanding the structure of the Internet graph is a crucial step for
building accurate network models and designing efficient algorithms for
Internet applications. Yet, obtaining its graph structure is a  
surprisingly
difficult task, as edges cannot be explicitly queried. Instead,  
empirical
studies rely on traceroutes to build what are essentially single-source,
all-destinations, shortest-path trees. These trees only sample a  
fraction of
the network's edges, and a recent paper by Lakhina et al. found  
empirically
that the resuting sample is intrinsically biased. For instance, the  
observed
degree distribution under traceroute sampling exhibits a power law  
even when
the underlying degree distribution is Poisson.
   In this paper, we study the bias of traceroute sampling  
systematically, and,
for a very general class of underlying degree distributions,  
calculate the
likely observed distributions explicitly. To do this, we use a  
continuous-time
realization of the process of exposing the BFS tree of a random graph  
with a
given degree distribution, calculate the expected degree distribution  
of the
tree, and show that it is sharply concentrated. As example  
applications of our
machinery, we show how traceroute sampling finds power-law degree  
distributions
in both delta-regular and Poisson-distributed random graphs. Thus,  
our work
puts the observations of Lakhina et al. on a rigorous footing, and  
extends them
to nearly arbitrary degree distributions.


http://front.math.ucdavis.edu/cond-mat/0503087

---------------------------------------------------------------

3321. THE CRITICAL ISING MODEL ON TREES, CONCAVE RECURSIONS AND  
NONLINEAR  CAPACITY

Robin Pemantle and Yuval Peres

We consider the Ising model on a general tree under various boundary
conditions: all plus, free and spin-glass. In each case, we determine  
when the
root is influenced by the boundary values in the limit as the  
boundary recedes
to infinity. We obtain exact capacity criteria that govern behavior  
at critical
temperatures. For plus boundary conditions, an $L^3$ capacity arises. In
particular, on a spherically symmetric tree that has $n^c b^n$  
vertices at
level $n$ (up to bounded factors), we prove that there is a unique Gibbs
measure for the ferromagnetic Ising model if and only if $c$ is at  
most 1/2.
Our proofs are based on a new link between nonlinear recursions on  
trees and
$L^p$ capacities.


http://front.math.ucdavis.edu/math.PR/0503137

---------------------------------------------------------------

3322. HOW LARGE A DISC IS COVERED BY A RANDOM WALK IN $N$ STEPS?

Amir Dembo and  Yuval Peres and Jay Rosen

We show that the largest disc covered by a simple random walk on the  
planar
square lattice after $n$ steps has radius $n^{1/4+o(1)}$, thus  
resolving an
open problem of P. R\'ev\'esz (1990). We also show that almost  
surely, for
infinitely many values of $n$ it takes about $n^{1/2+o(1)}$ steps  
after step
$n$ for the random walk to reach the first previously unvisited site  
(and the
exponent 1/2 is sharp). This resolves a problem raised by P. R\'ev 
\'esz (1993).
Additional results on multiple covering are obtained as well.


http://front.math.ucdavis.edu/math.PR/0503139

---------------------------------------------------------------

3323. INFINITE DIMENSIONAL STOCHASTIC DIFFERENTIAL EQUATIONS OF   
ORNSTEIN-UHLENBECK TYPE

Siva R. Athreya and  Richard F. Bass and  Maria Gordina and  Edwin A.  
Perkins

We consider the operator $$\sL f(x)=\tfrac12 \sum_{i,j=1}^\infty
a_{ij}(x)\frac{\del^2 f}{\del x_i \del x_j}(x)-\sum_{i=1}^\infty  
\lam_i x_i
b_i(x) \frac{\del f}{\del x_i}(x).$$ We prove existence and  
uniqueness of
solutions to the martingale problem for this operator under appropriate
conditions on the $a_{ij}, b_i$, and $\lam_i$. The process  
corresponding to
$\sL$ solves an infinite dimensional stochastic differential equation  
similar
to that for the infinite dimensional Ornstein-Uhlenbeck process.


http://front.math.ucdavis.edu/math.PR/0503165

---------------------------------------------------------------

3324. ON CHORDAL AND BILATERAL SLE IN MULTIPLY CONNECTED DOMAINS

Robert O. Bauer and  Roland M. Friedrich

We discuss the possible candidates for conformally invariant random
non-self-crossing curves which begin and end on the boundary of a  
multiply
connected planar domain, and which satisfy a Markovian-type property. We
consider both, the case when the curve connects a boundary component  
to itself
(chordal), and the case when the curve connects two different boundary
components (bilateral). We establish appropriate extensions of Loewner's
equation to multiply connected domains for the two cases. We show  
that a curve
in the domain induces a motion on the boundary and that this motion  
is enough
to first recover the motion of the moduli of the domain and then,  
second, the
curve in the interior. For random curves in the interior we show that  
the
induced random motion on the boundary is not Markov if the domain is  
multiply
connected, but that the random motion on the boundary together with  
the random
motion of the moduli forms a Markov process. In the chordal case, we  
show that
this Markov process satisfies Brownian scaling and discuss how this  
limits the
possible conformally invariant random non-self-crossing curves. We  
show that
the possible candidates are labeled by a real constant and a function
homogeneous of degree minus one which describes the interaction of  
the random
curve with the boundary. We show that the random curve has the locality
property if the interaction term vanishes and the real parameter  
equals six.


http://front.math.ucdavis.edu/math.PR/0503178

---------------------------------------------------------------

3325. FROM N-PARAMETER FRACTIONAL BROWNIAN MOTIONS TO N-PARAMETER   
MULTIFRACTIONAL BROWNIAN MOTIONS

E. Herbin

Multifractional Brownian motion is an extension of the well-known  
fractional
Brownian motion where the Holder regularity is allowed to vary along  
the paths.
In this paper, two kind of multi-parameter extensions of mBm are  
studied: one
is isotropic while the other is not. For each of these processes, a  
moving
average representation, a harmonizable representation, and the  
covariance
structure are given. The Holder regularity is then studied. In  
particular, the
case of an irregular exponent function H is investigated. In this  
situation,
the almost sure pointwise and local Holder exponents of the multi- 
parameter mBm
are proved to be equal to the correspondent exponents of H.  
Eventually, a local
asymptotic self-similarity property is proved. The limit process can  
be another
process than fBm.


http://front.math.ucdavis.edu/math.PR/0503182

---------------------------------------------------------------

3326. EXAMPLES OF GROUPS THAT ARE MEASURE EQUIVALENT TO THE FREE GROUP

Damien Gaboriau (UMPA-ENSL)

Measure Equivalence (ME) is the measure theoretic counterpart of
quasi-isometry. This field grew considerably during the last years,  
developing
tools to distinguish between different ME classes of countable  
groups. On the
other hand, contructions of ME equivalent groups are very rare. We  
present a
new method, based on a notion of measurable free-factor, and we apply  
it to
exhibit a new family of groups that are measure equivalent to the  
free group.
We also present a quite extensive survey on results about Measure  
Equivalence
for countable groups.


http://front.math.ucdavis.edu/math.DS/0503181

---------------------------------------------------------------

3327. ORTHOGONAL POLYNOMIALS AND FLUCTUATIONS OF RANDOM MATRICES

Timothy Kusalik and  James A. Mingo and  and Roland Speicher

In this paper we establish a connection between the fluctuations of  
Wishart
random matrices, shifted Chebyshev polynomials, and planar diagrams  
whose
linear span form a basis for the irreducible representations of the  
annular
Temperly-Lieb algebra.


http://front.math.ucdavis.edu/math.OA/0503169

---------------------------------------------------------------

3328. COUNTING CONNECTED GRAPHS ASYMPTOTICALLY

Remco van der Hofstad and  Joel Spencer

We find the asymptotic number of connected graphs with $k$ vertices and
$k-1+l$ edges when $k,l$ approach infinity, reproving a result of  
Bender,
Canfield and McKay. We use the {\em probabilistic method}, analyzing
breadth-first search on the random graph $G(k,p)$ for an appropriate  
edge
probability $p$. Central is analysis of a random walk with fixed  
beginning and
end which is tilted to the left.


http://front.math.ucdavis.edu/math.CO/0502579

---------------------------------------------------------------

3329. ON Q-FUNCTIONAL EQUATIONS AND EXCURSION MOMENTS

Christoph Richard

We analyse q-functional equations arising from tree-like combinatorial
structures, which are counted by size, internal path length and certain
generalisations thereof. The corresponding counting parameters are  
labelled by
an integer k>1. We show the existence of a joint limit distribution  
for these
parameters in the limit of infinite size, if the size generating  
function has a
square root as dominant singularity. The limit distribution coincides  
with that
of integrals of (k-1)th powers of the standard Brownian excursion.  
Our method
yields a recursion for the moments of the joint distribution and  
admits an
extension to other types of singularities.


http://front.math.ucdavis.edu/math.CO/0503198

---------------------------------------------------------------

3330. A SET-INDEXED FRACTIONAL BROWNIAN MOTION

E. Herbin and E. Merzbach

We define and prove the existence of a fractional Brownian motion  
indexed by
a collection of closed subsets of a measure space. This process is a
generalization of the set-indexed Brownian motion, when the condition of
independance is relaxed. Relations with the Levy fractional Brownian  
motion and
with the fractional Brownian sheet are studied. We prove stationarity  
of the
increments and a property of self-similarity with respect to the  
action of
solid motions. Regularity conditions are exhibited. Finally, behavior  
of the
set-indexed fractional Brownian motion along increasing paths is  
analysed.


http://front.math.ucdavis.edu/math.PR/0503211

---------------------------------------------------------------

3331. ENTROPY-DRIVEN PHASE TRANSITION IN A POLYDISPERSE HARD-RODS  
LATTICE  SYSTEM

Dmitry Ioffe and  Yvan Velenik (LMRS) and  Milos Zahradnik

We study a system of rods on the 2d square lattice, with hard-core  
exclusion.
Each rod has a length between 2 and N. We show that, when N is  
sufficiently
large, and for suitable fugacity, there are several distinct Gibbs  
states, with
orientational long-range order. This is in sharp contrast with the  
case N=2
(the monomer-dimer model), for which Heilmann and Lieb proved absence  
of phase
transition at any fugacity. This is the first example of a pure hard- 
core
system with phases displaying orientational order, but not  
translational order;
this is a fundamental characteristic feature of liquid crystals.


http://front.math.ucdavis.edu/math.PR/0503222

---------------------------------------------------------------

3332. AN INDUCTIVE PROOF OF THE BERRY-ESSEEN THEOREM FOR CHARACTER  
RATIOS

Jason Fulman

Bolthausen used a variation of Stein's method to give an inductive  
proof of
the Berry-Esseen theorem for sums of independent, identically  
distributed
random variables. We modify this technique to prove a Berry-Esseen  
theorem for
character ratios of a random representation of the symmetric group on
transpositions. An analogous result is proved for Jack measure on  
partitions.


http://front.math.ucdavis.edu/math.CO/0503227

---------------------------------------------------------------

3333. MAX-SEMI-SELFDECOMPOSABLE LAWS AND RELATED PROCESSES

S Satheesh and E Sandhya

Methods of construction of Max-semi-selfdecompsable laws are given.
Implications of this method in random time changed extremal processes  
are
discussed. Max-autoregressive model is introduced and characterized  
using the
max-semi-selfdecompsable laws and exponential max-semi-stable laws. Some
comments regarding the infinite divisibility of semi-stable and max- 
semi-stable
laws are given.


http://front.math.ucdavis.edu/math.PR/0503232

---------------------------------------------------------------

3334. DISCRETE INTERPOLATION BETWEEN MONOTONE PROBABILITY AND FREE  
PROBABILITY

Romuald Lenczewski and  Rafal Salapata

We construct a sequence of states called m-monotone product states  
which give
a discrete interpolation between the monotone product of states of  
Muraki and
the free product of states of Avitzour and Voiculescu in free  
probability. We
derive the associated basic limit theorems and develop the  
combinatorics based
on non-crossing ordered partitions with monotone order starting from  
depth m.
The Hilbert space representations of the limit mixed moments in the  
invariance
principle lead to m-monotone Gaussian operators living in m-monotone  
Fock
spaces, which are truncations of the free Fock space over the square- 
integrable
functions on the non-negative real line (m=1 gives the monotone Fock  
space). A
new type of combinatorics of inner blocks leads to explicit formulas  
for the
mixed moments of m-monotone Gaussian operators, which are new even in  
the case
of monotone independent Gaussian operators with arcsine distributions.


http://front.math.ucdavis.edu/math.QA/0502570

---------------------------------------------------------------

3335. RIFFLE SHUFFLES OF DECKS WITH REPEATED CARDS

Mark Conger and D. Viswanath

By a well-known result of Bayer and Diaconis, the maximum entropy  
model of
the common riffle shuffle implies that the number of riffle shuffles  
necessary
to mix a standard deck of 52 cards is either 7 or 11 -- with the  
former number
applying when the metric used to define mixing is the total variation  
distance
and the later when it is the separation distance. This and other related
results assume all 52 cards in the deck to be distinct and require  
all $52!$
permutations of the deck to be almost equally likely for the deck to be
considered well mixed. In many instances, not all cards in the deck are
distinct and only the sets of cards dealt out to players, and not the  
order in
which they are dealt out to each player, needs to be random. We derive
transition probabilities under riffle shuffles between decks with  
repeated
cards to cover some instances of the type just described. We focus on  
decks
with cards all of which are labeled either 1 or 2 and describe the  
consequences
of having a symmetric starting deck of the form $1,...,1,2...,2$ or  
$1,2,...,
1,2$. Finally, we consider mixing times for common card games.


http://front.math.ucdavis.edu/math.PR/0503233

---------------------------------------------------------------

3336. BERMUDAN OPTION PRICING BASED ON PIECEWISE HARMONIC  
INTERPOLATION AND  THE R\'EDUITE

Frederik S. Herzberg

We consider an iterative Bermudan option pricing algorithm based on  
piecewise
harmonic interpolation and give an explicit constructive  
characterisation of
the smallest fixed point of the iteration step as the approximate  
price of the
perpetual Bermudan option. The same arguments work for a related  
iterative
algorithm based on the approximation of subharmonic functions via the  
r\'eduite
associated with a given closed $F_{\sigma}$ subset of $\RR^d$.


http://front.math.ucdavis.edu/math.PR/0503234

---------------------------------------------------------------

3337. A BRIEF NOTE ON THE SOUNDNESS OF BERMUDAN OPTION PRICING VIA  
CUBATURE

Frederik S. Herzberg

The subject of this study is an iterative Bermudan option pricing  
algorithm
based on (high-dimensional) cubature. We show that the sequence of  
Bermudan
prices (as functions of the underlying assets' logarithmic start prices)
resulting from the iteration is bounded and increases monotonely to the
approximate perpetual Bermudan option price; the convergence is  
linear in the
supremum norm with the discount factor being the convergence factor.
Furthermore, we prove a characterisation of this approximated perpetual
Bermudan price as the smallest fixed point of the iteration procedure.


http://front.math.ucdavis.edu/math.PR/0503235

---------------------------------------------------------------

3338. SPHERICAL ASYMPTOTICS FOR THE ROTOR-ROUTER MODEL IN Z^D

Lionel Levine and  Yuval Peres

The rotor-router model is a deterministic analogue of random walk  
invented by
Jim Propp. It can be used to define a deterministic aggregation model  
analogous
to internal diffusion limited aggregation. We prove an isoperimetric  
inequality
for the exit time of simple random walk from a finite region in Z^d,  
and use
this to prove that the shape of the rotor-router aggregation model in  
Z^d,
suitably rescaled, converges to a Euclidean ball in R^d.


http://front.math.ucdavis.edu/math.PR/0503251

---------------------------------------------------------------

3339. SOME EXPLICIT KREIN REPRESENTATIONS OF CERTAIN SUBORDINATORS,  
INCLUDING  THE GAMMA PROCESS

Catherine Donati-Martin (PMA) and  Marc Yor (PMA)

We give a representation of the Gamma subordinator as a Krein  
functional of
Brownian motion, using the known representations for stable  
subordinators and
Esscher transforms. In particular, we have obtained Krein  
representations of
the subordinators which govern the two parameter Poisson-Dirichlet  
family of
distributions.


http://front.math.ucdavis.edu/math.PR/0503254

---------------------------------------------------------------

3340. AN INVARIANCE PRINCIPLE FOR CONDITIONED TREES

Jean-Francois Le Gall (DMA-ENS Paris)

We consider Galton-Watson trees associated with a critical offspring
distribution and conditioned to have exactly $n$ vertices. These  
trees are
embedded in the real line by affecting spatial positions to the  
vertices, in
such a way that the increments of the spatial positions along edges  
of the tree
are independent variables distributed according to a symmetric  
probability
distribution on the real line. We then condition on the event that  
all spatial
positions are nonnegative. Under suitable assumptions on the offspring
distribution and the spatial displacements, we prove that these  
conditioned
spatial trees converge as $n\to\infty$, modulo an appropriate rescaling,
towards the conditioned Brownian tree that was studied in previous work.
Applications are given to asymptotics for random quadrangulations.


http://front.math.ucdavis.edu/math.PR/0503263

---------------------------------------------------------------

3341. ON GENERALIZED COMPUTABLE UNIVERSAL PRIORS AND THEIR CONVERGENCE

Marcus Hutter

Solomonoff unified Occam's razor and Epicurus' principle of multiple
explanations to one elegant, formal, universal theory of inductive  
inference,
which initiated the field of algorithmic information theory. His  
central result
is that the posterior of the universal semimeasure M converges  
rapidly to the
true sequence generating posterior mu, if the latter is computable.  
Hence, M is
eligible as a universal predictor in case of unknown mu. The first  
part of the
paper investigates the existence and convergence of computable universal
(semi)measures for a hierarchy of computability classes: recursive,  
estimable,
enumerable, and approximable. For instance, M is known to be  
enumerable, but
not estimable, and to dominate all enumerable semimeasures. We  
present proofs
for discrete and continuous semimeasures. The second part  
investigates more
closely the types of convergence, possibly implied by universality: in
difference and in ratio, with probability 1, in mean sum, and for  
Martin-Loef
random sequences. We introduce a generalized concept of randomness for
individual sequences and use it to exhibit difficulties regarding  
these issues.
In particular, we show that convergence fails (holds) on generalized- 
random
sequences in gappy (dense) Bernoulli classes.


http://front.math.ucdavis.edu/cs.LG/0503026

---------------------------------------------------------------

3342. THE STABLE MANIFOLD THEOREM FOR SEMILINEAR STOCHASTIC  
EVOLUTION  EQUATIONS AND STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS I:  
THE STOCHASTIC
   SEMIFLOW

Salah-Eldin A Mohammed and  Tusheng Zhang and  Huaizhong Zhao

The main objective of this work is to characterize the pathwise local
structure of solutions of semilinear stochastic evolution equations  
(see's) and
stochastic partial differential equations (spde's) near stationary  
solutions.
Such characterization is realized through the long-term behavior of the
solution field near stationary points. The analysis falls in two  
parts I, II.
In Part I (this paper), we prove a general existence and compactness  
theorem
for $C^k$-cocycles of semilinear see's and spde's. Our results cover  
a large
class of semilinear see's as well as certain semilinear spde's with
non-Lipschitz terms such as stochastic reaction diffusion equations  
and the
stochastic Burgers equation with additive infinite-dimensional noise.  
In Part
II of this work ([M-Z-Z]), we establish a local stable manifold  
theorem for
non-linear see's and spde's.


http://front.math.ucdavis.edu/math.PR/0503320

---------------------------------------------------------------

3343. THE STABLE MANIFOLD THEOREM FOR SEMILINEAR STOCHASTIC  
EVOLUTION  EQUATIONS AND STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS  
II: EXISTENCE OF
   STABLE AND UNSTABLE MANIFOLDS

Salah-Eldin A. Mohammed and  Tusheng Zhang and  Huaizhong Zhao

This article is a sequel to [M.Z.Z.1] aimed at completing the
characterization of the pathwise local structure of solutions of  
semilinear
stochastic evolution equations (see's) and stochastic partial  
differential
equations (spde's) near stationary solutions. Stationary solution are  
viewed as
random points in the infinite-dimensional state space, and the  
characterization
is expressed in terms of the almost sure long-time behavior of  
trajectories of
the equation in relation to the stationary solution. More  
specifically, we
establish local stable manifold theorems for semilinear see's and spde's
(Theorems 4.1-4.4). These results give smooth stable and unstable  
manifolds in
the neighborhood of a hyperbolic stationary solution of the underlying
stochastic equation. The stable and unstable manifolds are  
stationary, live in
a stationary tubular neighborhood of the stationary solution and are
asymptotically invariant under the stochastic semiflow of the see/ 
spde. The
proof uses infinite-dimensional multiplicative ergodic theory  
techniques and
interpolation arguments (Theorem 2.1).


http://front.math.ucdavis.edu/math.PR/0503321

---------------------------------------------------------------

3344. BOUNDARY HARNACK PRINCIPLE FOR FRACTIONAL POWERS OF LAPLACIAN  
ON THE  SIERPINSKI CARPET

Andrzej Stos (LMP-Clermont)

We prove the Boundary Harnack Principle related to fractional powers of
Laplacian for some natural regions in the two-dimensional Sierpinski  
carpet.
This is a natual application of a probabilistic method based on the
Ikeda-Watanabe formula


http://front.math.ucdavis.edu/math.PR/0503333

---------------------------------------------------------------

3345. A NOTE ON EXACT LIKELIHOODS OF THE CARR-WU MODELS FOR LEVERAGE  
EFFECTS  AND VOLATILITY IN FINANCIAL ECONOMICS

Lancelot F. James

Recently Carr and Wu (2004, 2005) and also Huang and Wu (2004) show  
that most
stochastic processes used in traditional option pricing models can be  
cast as
special cases of time-changed L\'evy processes. In particular these  
are models
which can be tailored to exhibit correlated jumps in both the log  
price of
assets and the instantaneous volatility. Naturally similar to a  
recent work of
Barndorff-Nielsen and Shephard (2001a, b), such models may be used in a
likelihood based framework. These likelihoods are based on the  
unobserved
integrated volatility, rather than the instantaneous volatility.  
James (2005)
establishes general results for the likelihood and estimation of a  
large class
of such models which include possible leverage effects. In this note  
we show
that exact expressions for likelihood models based on generalizations  
of Carr
and Wu (2005) and Huang and Wu (2005), follow essentially from the  
arguments in
Theorem 5.1 in James (2005) with some slight modification. This  
serves to
formally verify a claim made by James (2005).


http://front.math.ucdavis.edu/math.ST/0503314

---------------------------------------------------------------

3346. POISSON KERNELS OF HALF-SPACES IN REAL HYPERBOLIC SPACES

T. Byczkowski and  P. Graczyk and  A. Stos

We provide an integral formula for the Poisson kernel of half-spaces for
Brownian motion in real hyperbolic space $\H^n$. This enables us to find
asymptotic properties of the kernel. Our starting point is the  
formula for its
Fourier transform. When $n=3$, 4 or 6 we give an explicit formula for  
the
Poisson kernel itself. In the general case we give various  
asymptotics and show
convergence to the Poisson kernel of $\H^n$.


http://front.math.ucdavis.edu/math.PR/0503372

---------------------------------------------------------------

3347. DOOB'S MAXIMAL IDENTITY, MULTIPLICATIVE DECOMPOSITIONS AND  
ENLARGEMENTS  OF FILTRATIONS

A. Nikeghbali and  M. Yor

In the theory of progressive enlargements of filtrations, the  
supermartingale
$Z_{t}=\mathbf{P}(g>t\mid \mathcal{F}_{t}) $ associated with an  
honest time
$g$, and its additive (Doob-Meyer) decomposition, play an essential  
role. In
this paper, we propose an alternative approach, using a multiplicative
representation for the supermartingale $Z_{t}$, based on Doob's maximal
identity. We thus give new examples of progressive enlargements.  
Moreover, we
give, in our setting, a proof of the decomposition formula for  
martingales,
using initial enlargement techniques, and use it to obtain some path
decompositions given the maximum or minimum of some processes.


http://front.math.ucdavis.edu/math.PR/0503386

---------------------------------------------------------------

3348. AN ANNIHILATING-BRANCHING PARTICLE MODEL FOR THE HEAT EQUATION  
WITH  AVERAGE TEMPERATURE ZERO

Krzysztof Burdzy and Jeremy Quastel

We consider two species of particles performing random walks in a  
domain in
Euclidean space with reflecting boundary conditions, which annihilate on
contact. In addition there is a conservation law so that the total  
number of
particles of each type is preserved: When the two particles of different
species annihilate each other, particles of each species, chosen at  
random,
give birth. We assume initially equal numbers of each species and  
show that the
system has a diffusive scaling limit in which the densities of the  
two species
are well approximated by the positive and negative parts of the  
solution of the
heat equation normalized to have constant $L^1$ norm. In particular,  
the higher
Neumann eigenfunctions appear as asymptotically stable states at the  
diffusive
time scale.


http://front.math.ucdavis.edu/math.PR/0503395

---------------------------------------------------------------

3349. THE REVERSIBLE NEAREST PARTICLE SYSTGEMS ON A FINITE INTERVAL

Dayue Chen and  Juxin Liu and  Fuxi Zhang

In this paper we study a one-parameter family of attractive reversible
nearest particle system on a finite interval. As the length of the  
interval
increases, the time that the nearest particle system first hits the  
empty set
increases in different order, from logarithmic to exponential,  
according to the
intensity of interaction. In particular, at the critical case, the first
hitting time increases in a polynomial order.


http://front.math.ucdavis.edu/math.PR/0503409

---------------------------------------------------------------

3350. INSIDE SINGULARITY SETS OF RANDOM GIBBS MEASURES

Julien Barral and  Stephane Seuret

We evaluate the scale at which the multifractal structure of some random
Gibbs measures becomes discernible. The value of this scale is  
obtained through
what we call the growth speed in H\"older singularity sets of a Borel  
measure.
This growth speed yields new information on the multifractal behavior  
of the
rescaled copies involved in the structure of statistically self- 
similar Gibbs
measures. Our results are useful to understand the multifractal  
nature of
various heterogeneous jump processes.


http://front.math.ucdavis.edu/math.PR/0503420

---------------------------------------------------------------

3351. RENEWAL OF SINGULARITY SETS OF STATISTICALLY SELF-SIMILAR MEASURES

Julien Barral and  Stephane Seuret

This paper investigates new properties concerning the multifractal  
structure
of a class of statistically self-similar measures. These measures  
include the
well-known Mandelbrot multiplicative cascades, sometimes called  
independent
random cascades. We evaluate the scale at which the multifractal  
structure of
these measures becomes discernible. The value of this scale is  
obtained through
what we call the growth speed in H\"older singularity sets of a Borel  
measure.
This growth speed yields new information on the multifractal behavior  
of the
rescaled copies involved in the structure of statistically self-similar
measures. Our results are useful to understand the multifractal  
nature of
various heterogeneous jump processes.


http://front.math.ucdavis.edu/math.PR/0503421

---------------------------------------------------------------

3352. A POLYHEDRAL MARKOV FIELD - PUSHING THE ARAK-SURGAILIS  
CONSTRUCTION INTO  THREE DIMENSIONS

Tomasz Schreiber

The purpose of the paper is to construct a polyhedral Markov field in
${\mathbb R}^3$ in analogy with the planar construction of the  
original Arak
(1982) polygonal Markov field. We provide a dynamic construction of  
the process
in terms of evolution of two-dimensional multi-edge systems tracing  
polyhedral
boundaries of the field in three-dimensional time-space. We also give  
a general
algorithm for simulating Gibbsian modifications of the constructed  
polyhedral
field.


http://front.math.ucdavis.edu/math.PR/0503429

---------------------------------------------------------------

3353. BAYSIAN INFERENCE VIA CLASSES OF NORMALIZED RANDOM MEASURES

Lancelot F. James and  Antonio Lijoi and Igor Pruenster

One of the main research areas in Bayesian Nonparametrics is the  
proposal and
study of priors which generalize the Dirichlet process. Here we exploit
theoretical properties of Poisson random measures in order to provide a
comprehensive Bayesian analysis of random probabilities which are  
obtained by
an appropriate normalization. Specifically we achieve explicit and  
tractable
forms of the posterior and the marginal distributions, including an  
explicit
and easily used description of generalizations of the important
Blackwell-MacQueen P\'olya urn distribution. Such simplifications are  
achieved
by the use of a latent variable which admits quite interesting  
interpretations
which allow to gain a better understanding of the behaviour of these  
random
probability measures. It is noteworthy that these models are  
generalizations of
models considered by Kingman (1975) in a non-Bayesian context. Such  
models are
known to play a significant role in a variety of applications including
genetics, physics, and work involving random mappings and assemblies.  
Hence our
analysis is of utility in those contexts as well. We also show how  
our results
may be applied to Bayesian mixture models and describe computational  
schemes
which are generalizations of known efficient methods for the case of the
Dirichlet process. We illustrate new examples of processes which can  
play the
role of priors for Bayesian nonparametric inference and finally point  
out some
interesting connections with the theory of generalized gamma  
convolutions
initiated by Thorin and further developed by Bondesson.


http://front.math.ucdavis.edu/math.ST/0503394

---------------------------------------------------------------

3354. A STOCHASTIC APPROXIMATION ALGORITHM WITH MULTIPLICATIVE STEP  
SIZE  ADAPTATION

Alexander Plakhov and  Pedro Cruz

An algorithm of searching a zero of an unknown undimensional function is
considered, measured at a point x with some error. The step sizes are  
random
positive values and are calculated according to the rule: if two  
consecutive
iterations are in same direction step is multiplied by u>1,  
otherwise, it is
multiplied by 0<d<1. The function may have one or more zeros; the  
random values
are independent and identically distributed, with zero mean and finite
variance. Under some additional assumptions on the conditions on the two
parameters u and d almost sure convergence of the sequence as well as  
under
some conditions is guaranteed almost sure divergence. In particular,  
if the
error distribuition as median 0 and zero probability for particular  
poinst then
it is established that for ud<1, convergence takes place, and for ud>1,
divergence. Due to the multiplicative rule of updating of the step,  
it is
natural to expect that the sequence converges rapidly: like a geometric
progression (if convergence takes place), but the limit value may not  
coincide
with, but instead, approximates one of zeros of the function. By  
adjusting the
parameters u and d, one can reach necessary precision of  
approximation; higher
precision is obtained at the expense of lower convergence rate.


http://front.math.ucdavis.edu/math.ST/0503434

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3355. ON APPROXIMATE PATTERN MATCHING FOR A CLASS OF GIBBS RANDOM FIELDS

J.R. Chazottes and  F. Redig and  E. Verbitskiy

We prove an exponential approximation for the law of approximate  
occurrence
of typical patterns for a class of Gibbsian sources on the lattice $ 
\mathbb
Z^d$, $d\ge 2$. From this result, we deduce a law of large numbers  
and a large
deviation result for the the waiting time of distorted patterns.


http://front.math.ucdavis.edu/math.PR/0503008

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3356. THE BASIC REPRESENTATION OF THE CURRENT GROUP O(N,1)^X IN THE  
L^2 SPACE  OVER THE GENERALIZED LEBESGUE MEASURE

A.M.Vershik and  M.I.Graev

We give the realization of the representation of the current group O 
(n,1)^X
where X is a manifold, in the Hilbert space of L^2(F,\nu) of  
functionals on the
the space F of the generalized functions on the manifold X which are  
square
integrable over measure \nu which is related to a distinguish Levy  
process with
values in R^{n-1} which generalized one dimensional gamma process.  
Unipotent
subgroup of the group O(n,1)^X acts as the group of multiplicators.  
Measure \nu
is sigma-finite and invariant under the action current group O(n-1) 
^X. Ther
case of n=2 (SL(2,R^X)) was considered before in the series of papers  
starting
from the article Vershik-Gel'fand-Graev (1973).


http://front.math.ucdavis.edu/math.RT/0503404

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3357. DYNAMIC IMPORTANCE SAMPLING FOR UNIFORMLY RECURRENT MARKOV CHAINS

Paul Dupuis and Hui Wang

Importance sampling is a variance reduction technique for efficient
estimation of rare-event probabilities by Monte Carlo. In standard  
importance
sampling schemes, the system is simulated using an a priori fixed  
change of
measure suggested by a large deviation lower bound analysis. Recent  
work,
however, has suggested that such schemes do not work well in many  
situations.
In this paper we consider dynamic importance sampling in the setting of
uniformly recurrent Markov chains. By ``dynamic'' we mean that in the  
course of
a single simulation, the change of measure can depend on the outcome  
of the
simulation up till that time. Based on a control-theoretic approach  
to large
deviations, the existence of asymptotically optimal dynamic schemes is
demonstrated in great generality. The implementation of the dynamic  
schemes is
carried out with the help of a limiting Bellman equation. Numerical  
examples
are presented to contrast the dynamic and standard schemes.


http://front.math.ucdavis.edu/math.PR/0503454

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3358. THE EXIT PROBLEM FOR DIFFUSIONS WITH TIME-PERIODIC DRIFT AND  
STOCHASTIC  RESONANCE

Samuel Herrmann and Peter Imkeller

Physical notions of stochastic resonance for potential diffusions in
periodically changing double-well potentials such as the spectral power
amplification have proved to be defective. They are not robust for  
the passage
to their effective dynamics: continuous-time finite-state Markov chains
describing the rough features of transitions between different  
domains of
attraction of metastable points. In the framework of one-dimensional  
diffusions
moving in periodically changing double-well potentials we design a  
new notion
of stochastic resonance which refines Freidlin's concept of quasi- 
periodic
motion. It is based on exact exponential rates for the transition  
probabilities
between the domains of attraction which are robust with respect to  
the reduced
Markov chains. The quality of periodic tuning is measured by the  
probability
for transition during fixed time windows depending on a time scale  
parameter.
Maximizing it in this parameter produces the stochastic resonance  
points.


http://front.math.ucdavis.edu/math.PR/0503455

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3359. LEARNING MIXTURES OF SEPARATED NONSPHERICAL GAUSSIANS

Sanjeev Arora and Ravi Kannan

Mixtures of Gaussian (or normal) distributions arise in a variety of
application areas. Many heuristics have been proposed for the task of  
finding
the component Gaussians given samples from the mixture, such as the EM
algorithm, a local-search heuristic from Dempster, Laird and Rubin  
[J. Roy.
Statist. Soc. Ser. B 39 (1977) 1-38]. These do not provably run in  
polynomial
time. We present the first algorithm that provably learns the component
Gaussians in time that is polynomial in the dimension. The Gaussians  
may have
arbitrary shape, but they must satisfy a ``separation condition''  
which places
a lower bound on the distance between the centers of any two component
Gaussians. The mathematical results at the heart of our proof are  
``distance
concentration'' results--proved using isoperimetric inequalities--which
establish bounds on the probability distribution of the distance  
between a pair
of points generated according to the mixture. We also formalize the more
general problem of max-likelihood fit of a Gaussian mixture to  
unstructured
data.


http://front.math.ucdavis.edu/math.PR/0503457

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3360. FAST SIMULATION OF NEW COINS FROM OLD

Serban Nacu and Yuval Peres

Let S\subset (0,1). Given a known function f:S\to (0,1), we consider the
problem of using independent tosses of a coin with probability of  
heads p
(where p\in S is unknown) to simulate a coin with probability of  
heads f(p). We
prove that if S is a closed interval and f is real analytic on S,  
then f has a
fast simulation on S (the number of p-coin tosses needed has exponential
tails). Conversely, if a function f has a fast simulation on an open  
set, then
it is real analytic on that set.


http://front.math.ucdavis.edu/math.PR/0503458

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3361. STRUCTURE OF LARGE RANDOM HYPERGRAPHS

R. W. R. Darling and J. R. Norris

The theme of this paper is the derivation of analytic formulae for  
certain
large combinatorial structures. The formulae are obtained via fluid  
limits of
pure jump-type Markov processes, established under simple conditions  
on the
Laplace transforms of their Levy kernels. Furthermore, a related  
Gaussian
approximation allows us to describe the randomness which may persist  
in the
limit when certain parameters take critical values. Our method is quite
general, but is applied here to vertex identifiability in random  
hypergraphs. A
vertex v is identifiable in n steps if there is a hyperedge  
containing v all of
whose other vertices are identifiable in fewer steps.
   We say that a hyperedge is identifiable if every one of its  
vertices is
identifiable. Our analytic formulae describe the asymptotics of the  
number of
identifiable vertices and the number of identifiable hyperedges for a
Poisson(\beta) random hypergraph \Lambda on a set V of N vertices, in  
the limit
as N\to \infty. Here \beta is a formal power series with nonnegative
coefficients \beta_0,\beta_1,..., and (\Lambda(A))_{A\subseteq V} are
independent Poisson random variables such that \Lambda(A), the number of
hyperedges on A, has mean N\beta_j/\pmatrixN j whenever |A|=j.


http://front.math.ucdavis.edu/math.PR/0503460

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3362. LARGE DEVIATIONS FOR TEMPLATE MATCHING BETWEEN POINT PROCESSES

Zhiyi Chi

We study the asymptotics related to the following matching criteria  
for two
independent realizations of point processes X\sim X and Y\sim Y.  
Given l>0,
X\cap [0,l) serves as a template. For each t>0, the matching score  
between the
template and Y\cap [t,t+l) is a weighted sum of the Euclidean  
distances from
y-t to the template over all y\in Y\cap [t,t+l). The template  
matching criteria
are used in neuroscience to detect neural activity with certain  
patterns. We
first consider W_l(\theta), the waiting time until the matching score  
is above
a given threshold \theta. We show that whether the score is scalar- or
vector-valued, (1/l)\log W_l(\theta) converges almost surely to a  
constant
whose explicit form is available, when X is a stationary ergodic  
process and Y
is a homogeneous Poisson point process. Second, as l\to\infty, a strong
approximation for -\log [\Pr{W_l(\theta)=0}] by its rate function is
established, and in the case where X is sufficiently mixing, the  
rates, after
being centered and normalized by \sqrtl, satisfy a central limit  
theorem and
almost sure invariance principle. The explicit form of the variance  
of the
normal distribution is given for the case where X is a homogeneous  
Poisson
process as well.


http://front.math.ucdavis.edu/math.PR/0503463

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3363. RANDOM K-SAT: TWO MOMENTS SUFFICE TO CROSS A SHARP THRESHOLD

Dimitris Achlioptas and Cristopher Moore

Many NP-complete constraint satisfaction problems appear to undergo a  
"phase
transition'' from solubility to insolubility when the constraint  
density passes
through a critical threshold. In all such cases it is easy to derive  
upper
bounds on the location of the threshold by showing that above a  
certain density
the first moment (expectation) of the number of solutions tends to  
zero. We
show that in the case of certain symmetric constraints, considering  
the second
moment of the number of solutions yields nearly matching lower bounds  
for the
location of the threshold. Specifically, we prove that the threshold  
for both
random hypergraph 2-colorability (Property B) and random Not-All- 
Equal k-SAT is
2^{k-1} ln 2 -O(1). As a corollary, we establish that the threshold  
for random
k-SAT is of order Theta(2^k), resolving a long-standing open problem.


http://front.math.ucdavis.edu/cond-mat/0310227

---------------------------------------------------------------

3364. DISTRIBUTION OF THE SIZE OF A LARGEST PLANAR MATCHING AND  
LARGEST PLANAR  SUBGRAPH IN RANDOM BIPARTITE GRAPHS

Marcos Kiwi and  Martin Loebl

We address the following question: When a randomly chosen regular  
bipartite
multi--graph is drawn in the plane in the ``standard way'', what is the
distribution of its maximum size planar matching (set of non-- 
crossing disjoint
edges) and maximum size planar subgraph (set of non--crossing edges  
which may
share endpoints)? The problem is a generalization of the Longest  
Increasing
Sequence (LIS) problem (also called Ulam's problem). We present  
combinatorial
identities which relate the number of $r$-regular bipartite multi-- 
graphs with
maximum planar matching (maximum planar subgraph)of at most $d$ edges  
to a
signed sum of restricted lattice walks in $\ZZ^d$, and to the number  
of pairs
of standard Young tableaux of the same shape and with a ``descend-- 
type''
property. Our results are obtained via generalizations of two  
combinatorial
proofs through which Gessel's identity can be obtained (an identity  
that is
crucial in the derivation of a bivariate generating function  
associated to the
distribution of LISs, and key to the analytic attack on Ulam's problem).


http://front.math.ucdavis.edu/math.CO/0503465

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3365. THE SHANNON INFORMATION OF FILTRATIONS AND THE ADDITIONAL  
LOGARITHMIC  UTILITY OF INSIDERS

Stefan Ankirchner and  Steffen Dereich and Peter Imkeller

The background for the general mathematical link between utility and
information theory investigated in this paper is a simple financial  
market
model with two kinds of small traders: less informed traders and  
insiders,
whose extra information is represented by an enlargement of the other  
agents'
filtration. The expected logarithmic utility increment, i.e. the  
difference of
the insider's and the less informed trader's expected logarithmic  
utility is
described in terms of the information drift, i.e. the drift one has to
eliminate in order to perceive the price dynamics as a martingale  
from the
insider's perspective. On the one hand, we describe the information  
drift in a
very general setting by natural quantities expressing the  
probabilistic better
informed view of the world. This on the other hand allows us to  
identify the
additional utility by entropy related quantities known from  
information theory.
In particular, in a complete market in which the insider has some fixed
additional information during the entire trading interval, its utility
increment can be represented by the Shannon information of his extra  
knowledge.
For general markets, and in some particular examples, we provide  
estimates of
maximal utility by information inequalities.


http://front.math.ucdavis.edu/math.PR/0503013

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3366. DIFFUSION MAPS, SPECTRAL CLUSTERING AND REACTION COORDINATES  
OF  DYNAMICAL SYSTEMS

Boaz Nadler and  Stephane Lafon and  Ronald R. Coifman and  Ioannis  
G. Kevrekidis

A central problem in data analysis is the low dimensional  
representation of
high dimensional data, and the concise description of its underlying  
geometry
and density. In the analysis of large scale simulations of complex  
dynamical
systems, where the notion of time evolution comes into play,  
important problems
are the identification of slow variables and dynamically meaningful  
reaction
coordinates that capture the long time evolution of the system. In  
this paper
we provide a unifying view of these apparently different tasks, by  
considering
a family of {\em diffusion maps}, defined as the embedding of complex  
(high
dimensional) data onto a low dimensional Euclidian space, via the  
eigenvectors
of suitably defined random walks defined on the given datasets.  
Assuming that
the data is randomly sampled from an underlying general probability
distribution $p(\x)=e^{-U(\x)}$, we show that as the number of  
samples goes to
infinity, the eigenvectors of each diffusion map converge to the  
eigenfunctions
of a corresponding differential operator defined on the support of the
probability distribution. Different normalizations of the Markov  
chain on the
graph lead to different limiting differential operators. One  
normalization
gives the Fokker-Planck operators with the same potential U(x), best  
suited for
the study of stochastic differential equations as well as for  
clustering.
Another normalization gives the Laplace-Beltrami (heat) operator on the
manifold in which the data resides, best suited for the analysis of the
geometry of the dataset, regardless of its possibly non-uniform density.


http://front.math.ucdavis.edu/math.NA/0503445

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3367. TRADING STRATEGY ADIPTED OPTIMIZATION OF EUROPEAN CALL OPTION

Toshio Fukumi

Optimal pricing of European call option is described by linear  
stochastic
differential equation. Trading strategy given by a twin of stochastic  
variables
was integrated w.r.t. Black-Scholes formula to adopt optimal pricing to
tarading strategy.


http://front.math.ucdavis.edu/math.OC/0503444

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3368. CHARACTERIZATION OF ARBITRAGE-FREE MARKETS

Eva Strasser

The present paper deals with the characterization of no-arbitrage  
properties
of a continuous semimartingale. The first main result, Theorem
\refMainTheoremCharNA, extends the no-arbitrage criterion by Levental  
and
Skorohod [Ann. Appl.
   Probab. 5 (1995) 906-925] from diffusion processes to arbitrary  
continuous
semimartingales. The second main result, Theorem 2.4, is a  
characterization of
a weaker notion of no-arbitrage in terms of the existence of  
supermartingale
densities. The pertaining weaker notion of no-arbitrage is equivalent  
to the
absence of immediate arbitrage opportunities, a concept introduced by  
Delbaen
and Schachermayer [Ann. Appl. Probab. 5 (1995) 926-945]. Both results  
are
stated in terms of conditions for any semimartingales starting at  
arbitrary
stopping times \sigma. The necessity parts of both results are known  
for the
stopping time \sigma=0 from Delbaen and Schachermayer [Ann. Appl.  
Probab. 5
(1995) 926-945]. The contribution of the present paper is the proofs  
of the
corresponding sufficiency parts.


http://front.math.ucdavis.edu/math.PR/0503473

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3369. GAUSSIAN LIMITS FOR RANDOM MEASURES IN GEOMETRIC PROBABILITY

Yu. Baryshnikov and J. E. Yukich

We establish Gaussian limits for general measures induced by binomial  
and
Poisson point processes in d-dimensional space. The limiting Gaussian  
field has
a covariance functional which depends on the density of the point  
process. The
general results are used to deduce central limit theorems for  
measures induced
by random graphs (nearest neighbor, Voronoi and sphere of influence  
graph),
random sequential packing models (ballistic deposition and spatial  
birth-growth
models) and statistics of germ-grain models.


http://front.math.ucdavis.edu/math.PR/0503474

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3370. ON THE DISTRIBUTION OF THE MAXIMUM OF A GAUSSIAN FIELD WITH D  
PARAMETERS

Jean-Marc Azais and Mario Wschebor

Let I be a compact d-dimensional manifold, let X:I\to R be a Gaussian  
process
with regular paths and let F_I(u), u\in R, be the probability  
distribution
function of sup_{t\in I}X(t). We prove that under certain regularity and
nondegeneracy conditions, F_I is a C^1-function and satisfies a certain
implicit equation that permits to give bounds for its values and to  
compute its
asymptotic behavior as u\to +\infty. This is a partial extension of  
previous
results by the authors in the case d=1. Our methods use strongly the  
so-called
Rice formulae for the moments of the number of roots of an equation  
of the form
Z(t)=x, where Z:I\to R^d is a random field and x is a fixed point in  
R^d. We
also give proofs for this kind of formulae, which have their own  
interest
beyond the present application.


http://front.math.ucdavis.edu/math.PR/0503475

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3371. HEAVY TRAFFIC ANALYSIS OF OPEN PROCESSING NETWORKS WITH  
COMPLETE  RESOURCE POOLING: ASYMPTOTIC OPTIMALITY OF DISCRETE REVIEW  
POLICIES

Baris Ata and Sunil Kumar

We consider a class of open stochastic processing networks, with  
feedback
routing and overlapping server capabilities, in heavy traffic. The  
networks we
consider satisfy the so-called complete resource pooling condition and
therefore have one-dimensional approximating Brownian control problems.
   We propose a simple discrete review policy for controlling such  
networks.
   Assuming 2+\epsilon moments on the interarrival times and  
processing times,
we provide a conceptually simple proof of asymptotic optimality of  
the proposed
policy.


http://front.math.ucdavis.edu/math.PR/0503477

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3372. A CHARACTERIZATION OF THE OPTIMAL RISK-SENSITIVE AVERAGE COST  
IN FINITE  CONTROLLED MARKOV CHAINS

Rolando Cavazos-Cadena and Daniel Hernandez-Hernandez

This work concerns controlled Markov chains with finite state and action
spaces. The transition law satisfies the simultaneous Doeblin  
condition, and
the performance of a control policy is measured by the (long-run)
risk-sensitive average cost criterion associated to a positive, but  
otherwise
arbitrary, risk sensitivity coefficient. Within this context, the  
optimal
risk-sensitive average cost is characterized via a minimization  
problem in a
finite-dimensional Euclidean space.


http://front.math.ucdavis.edu/math.PR/0503478

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3373. LARGE DEVIATIONS OF THE EMPIRICAL VOLUME FRACTION FOR  
STATIONARY POISSON  GRAIN MODELS

Lothar Heinrich

We study the existence of the (thermodynamic) limit of the scaled
cumulant-generating function L_n(z)=|W_n|^{-1}\logE\exp{z|\Xi\cap  
W_n|} of the
empirical volume fraction |\Xi\cap W_n|/|W_n|, where |\cdot| denotes the
d-dimensional Lebesgue measure. Here \Xi=\bigcup_{i\ge1}(\Xi_i+X_i)  
denotes a
d-dimensional Poisson grain model (also known as a Boolean model)  
defined by a
stationary Poisson process \Pi_{\lambda}=\sum_{i\ge1}\delta_{X_i} with
intensity \lambda >0 and a sequence of independent copies \Xi_1, 
\Xi_2,... of a
random compact set \Xi_0. For an increasing family of compact convex  
sets {W_n,
n\ge1} which expand unboundedly in all directions, we prove the  
existence and
analyticity of the limit lim_{n\to\infty}L_n(z) on some disk in the  
complex
plane whenever E\exp{a|\Xi_0|}<\infty for some a>0. Moreover, closely  
connected
with this result, we obtain exponential inequalities and the exact  
asymptotics
for the large deviation probabilities of the empirical volume  
fraction in the
sense of Cram\'er and Chernoff.


http://front.math.ucdavis.edu/math.PR/0503479


From pas at www.economia.unimi.it  Fri Jul  1 22:56:28 2005
From: pas at www.economia.unimi.it (pas@www.economia.unimi.it)
Date: Fri Jul  1 22:58:52 2005
Subject: [Pas] Probabilty Abstracts 87b
Message-ID: <184043AE-56BB-4270-B946-774E9C9BAA4B@unimi.it>

                                                                         
                          July 1, 2005
                                                                         
                          Letter 87b


Apologizes for this second mail.
Previous PAS Letter 87 contained abstracts from Letter 86.

stefano iacus





Probability Abstract Service



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3374. FOKKER-PLANCK-KOLMOGOROV EQUATION FOR STOCHASTIC DIFFERENTIAL  
EQUATIONS  WITH BOUNDARY HITTING RESETS

Julien Bect and  Hana Baili and  Gilles Fleury

We consider a Markov process on a Riemannian manifold, which solves a
stochastic differential equation in the interior of the manifold and  
jumps
according to a deterministic reset map when it reaches the boundary.  
We derive
a partial differential equation for the probability density function,  
involving
a non-local boundary condition which accounts for the jumping  
behaviour of the
process. This is a generalisation of the usual Fokker-Planck-Kolmogorov
equation for diffusion processes. The result is illustrated with an  
example in
the field of stochastic hybrid systems.


http://front.math.ucdavis.edu/math.PR/0504583

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3375. SKEW CONVOLUTION SEMIGROUPS AND AFFINE MARKOV PROCESSES

D.A. Dawson (Carleton University) and  Zenghu Li (Beijing Normal   
University)

A general affine Markov semigroup is formulated as the convolution of a
homogeneous one with a skew convolution semigroup. We provide some  
sufficient
conditions for the regularities of the homogeneous affine semigroup  
and the
skew convolution semigroup. The corresponding affine Markov process is
constructed as the strong solution of a system of stochastic  
equations with
non-Lipschitz coefficients and Poisson-type integrals over some  
random sets.
Based on this characterization, it is proved that the affine process  
arises
naturally in a limit theorem for the difference of a pair of reactant  
processes
in a catalytic branching system with immigration.


http://front.math.ucdavis.edu/math.PR/0505444

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3376. A PROBABILISTIC REPRESENTATION FOR THE SOLUTIONS TO SOME NON- 
LINEAR PDES  USING PRUNED BRANCHING TREES

D. Bloemker and  M. Romito and  R. Tribe

The solutions to a large class of semi-linear parabolic PDEs are  
given in
terms of expectations of suitable functionals of a tree of branching  
particles.
A sufficient, and in some cases necessary, condition is given for the
integrability of the stochastic representation, using a companion  
scalar PDE.
   In cases where the representation fails to be integrable a  
sequence of pruned
trees is constructed, producing a approximate stochastic  
representations that
in some cases converge, globally in time, to the solution of the  
original PDE.


http://front.math.ucdavis.edu/math.PR/0505449

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3377. A LARGE-DEVIATIONS ANALYSIS OF THE GI/GI/1 SRPT QUEUE

Misja Nuyens and  Bert Zwart

We consider a GI/GI/1 queue with the shortest remaining processing time
discipline (SRPT) and light-tailed service times. Our interest is  
focused on
the tail behavior of the sojourn-time distribution. We obtain a general
expression for its large-deviations decay rate. The value of this  
decay rate
critically depends on whether there is mass in the endpoint of the  
service-time
distribution or not. An auxiliary priority queue, for which we obtain  
some new
results, plays an important role in our analysis. We apply our SRPT- 
results to
compare SRPT with FIFO from a large-deviations point of view.


http://front.math.ucdavis.edu/math.PR/0505450

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3378. HOW BADLY ARE THE BURHOLDER-DAVIS-GUNDY INEQUALITIES AFFECTED  
BY  ARBITRARY RANDOM TIMES?

Ashkan Nikeghbali

This note deals with the question: what remains of the Burkholder- 
Davis-Gundy
inequalities when stopping times $T$ are replaced by arbitrary random  
times
$\rho $? We prove that these inequalities still hold when $T$ is a
pseudo-stopping time and never holds for ends of predictable sets.


http://front.math.ucdavis.edu/math.PR/0505483

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3379. THE GHIRLANDA-GUERRA IDENTITIES

Pierluigi Contucci and  Cristian Giardina'

If the variance of a Gaussian spin-glass Hamiltonian grows like the  
volume
the model fulfills the Ghirlanda-Guerra identities in terms of the  
normalized
Hamiltonian covariance.


http://front.math.ucdavis.edu/math-ph/0505055

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3380. POSITIVE PROCESSES

V.I.Bakhtin

In the present paper we introduce positive flows and processes, which
generalize the ordinary dynamical systems and stochastic processes.  
We develop
a branch of theory of positive operators based on the concepts of  
phase and
positive algebras, the spectral potential, the dual entropy, equilibrium
measures, the action functional, sensitive states, empirical measures  
and prove
within it the law of large numbers with respect to the sensitive  
states and
calculate asymptotics for probabilities of large deviations in terms  
of the
action functional.


http://front.math.ucdavis.edu/math.DS/0505446

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3381. A LARGE CLOSED QUEUEING NETWORK CONTAINING TWO TYPES OF NODE  
AND  MULTIPLE CUSTOMER CLASSES: ONE BOTTLENECK STATION

Vyacheslav M. Abramov

The paper studies a closed queueing network containing two types of  
node. The
first type (server station) is an infinite server queueing system,  
and the
second type (client station) is a single server queueing system with  
autonomous
service, i.e. every client station serves customers (units) only at  
random
instants generated by strictly stationary and ergodic sequence of random
variables. It is assumed that there are $r$ server stations. At the  
initial
time moment all units are distributed in the server stations, and the  
$i$th
server station contains $N_i$ units, $i=1,2,...,r$, where all the  
values $N_i$
are large numbers of the same order. The total number of client  
stations is
equal to $k$. The expected times between departures in the client  
stations are
small values of the order $O(N^{-1})$ ~ $(N=N_1+N_2+...+N_r)$. After  
service
completion in the $i$th server station a unit is transmitted to the $j 
$th
client station with probability $p_{i,j}$ ~ ($j=1,2,...,k$), and  
being served
in the $j$th client station the unit returns to the $i$th server  
station. Under
the assumption that only one of the client stations is a bottleneck  
node, i.e.
the expected number of arrivals per time unit to the node is greater  
than the
expected number of departures from that node, the paper derives the
representation for non-stationary queue-length distributions in non- 
bottleneck
client stations.


http://front.math.ucdavis.edu/math.PR/0505489

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3382. CONCENTRATION FOR INDEPENDENT RANDOM VARIABLES WITH HEAVY TAILS

Franck Barthe (LSProba) and  Patrick Cattiaux (MODAL'X and  CMAP)  
and  Cyril  Roberto (LAMA)

If a random variable is not exponentially integrable, it is known  
that no
concentration inequality holds for an infinite sequence of  
independent copies.
Under mild conditions, we establish concentration inequalities for  
finite
sequences of $n$ independent copies, with good dependence in $n$.


http://front.math.ucdavis.edu/math.PR/0505492

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3383. A CONTINUOUS-DISCONTINUOUS SECOND-ORDER TRANSITION IN THE  
SATISFIABILITY  OF RANDOM HORN-SAT FORMULAS

Cristopher Moore and  Gabriel Istrate and  Demetrios Demopoulos and   
and Moshe Y.  Vardi

We compute the probability of satisfiability of a class of random  
Horn-SAT
formulae, motivated by a connection with the nonemptiness problem of  
finite
tree automata. In particular, when the maximum clause length is 3,  
this model
displays a curve in its parameter space along which the probability of
satisfiability is discontinuous, ending in a second-order phase  
transition
where it becomes continuous. This is the first case in which a phase  
transition
of this type has been rigorously established for a random constraint
satisfaction problem.


http://front.math.ucdavis.edu/math.PR/0505032

---------------------------------------------------------------

3384. SINAI'S CONDITION FOR REAL VALUED L\'{E}VY PROCESSES

Victor Rivero (MODAL'X)

We prove that the upward ladder height subordinator $H$ associated to  
a real
valued L\'{e}vy process $\xi$ has Laplace exponent $\phi$ that varies  
regularly
at $\infty$ (resp. at 0) if and only if the underlying L\'{e}vy  
process $\xi$
satisfies Sinai's condition at 0 (resp. at $\infty$). Sinai's  
condition for
real valued L\'{e}vy processes is the continuous time analogue of  
Sinai's
condition for random walks. We provide several criteria in terms of the
characteristics of $\xi$ to determine whether or not it satisfies  
Sinai's
condition. Some of these criteria are deduced from tail estimates of the
L\'{e}vy measure of $H,$ here obtained, and which are analogous to the
estimates of the tail distribution of the ladder height random  
variable of a
random walk which are due to Veraverbeke and Gr\"{u}bel


http://front.math.ucdavis.edu/math.PR/0505495

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3385. TRANSLATION-INVARIANT GENERALIZED TOPOLOGIES INDUCED BY  
PROBABILISTIC  NORMS

Bernardo Lafuerza-Guillen and Jose L. Rodriguez

In this paper we consider probabilistic normed spaces as defined by  
Alsina,
Sklar, and Schweizer, but equipped with non necessarily continuous  
triangle
functions. Such spaces endow a generalized topology that is
Fr\'echet-separable, translation-invariant and countably generated by  
radial
and circled 0-neighborhoods. Conversely, we show that such generalized
topologies are probabilistically normable.


http://front.math.ucdavis.edu/math.GN/0505484

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3386. A CLASS OF REMARKABLE SUBMARTINGALES (I)

Ashkan Nikeghbali

In this paper, we consider the special class of positive local  
submartingales
$(X_{t})$ of the form: $X_{t}=N_{t}+A_{t}$, where the measure $(dA_ 
{t})$ is
carried by the set ${t: X_{t}=0}$. We show that many examples of  
stochastic
processes studied in the literature are in this class and propose a  
unified
approach based on martingale techniques to study them. In particular, we
establish some martingale characterizations for these processes and  
compute
explicitly some distributions involving the pair $(X_{t},A_{t})$. We  
also
associate with $X$ a solution to the Skorokhod's stopping problem for
probability measures on the positive half-line.


http://front.math.ucdavis.edu/math.PR/0505515

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3387. PERFECTLY RANDOM SAMPLING OF TRUNCATED MULTINORMAL DISTRIBUTIONS

Pedro J. Fernandez and  Pablo A. Ferrari and  Sebastian Grynberg

A "coupling from the past" construction of the Gibbs sampler process  
is used
to perfectly simulate a random vector in a box B, a Cartesian product of
bounded intervals. An algorithm to sample vectors with multinormal  
distribution
truncated to B is implemented.


http://front.math.ucdavis.edu/math.PR/0505522

---------------------------------------------------------------

3388. A POINT PROCESS DESCRIBING THE COMPONENT SIZES IN THE CRITICAL  
WINDOW OF  THE RANDOM GRAPH EVOLUTION

Svante Janson and  Joel Spencer

We study a point process describing the asymptotic behavior of sizes  
of the
largest components of the random graph G(n,p) in the critical window
p=n^{-1}+lambda n^{-4/3}. In particular, we show that this point  
process has a
surprising rigidity. Fluctuations in the large values will be  
balanced by
opposite fluctuations in the small values such that the sum of the  
values
larger than a small epsilon is almost constant.


http://front.math.ucdavis.edu/math.PR/0505529

---------------------------------------------------------------

3389. SPECTRAL GAP ESTIMATES FOR INTERACTING PARTICLE SYSTEMS VIA A  
BAKRY &  EMERY-TYPE APPROACH

Anne-Severine Boudou and  Pietro Caputo and  Paolo Dai Pra and  
Gustavo Posta

We develop a general technique, based on the Bakry-Emery approach, to
estimate spectral gaps of a class of Markov operators. We apply this  
technique
to various interacting particle systems. In particular, we give a  
simple and
short proof of the diffusive scaling of the spectral gap of the  
Kawasaki model
at high temperature. Similar results are derived for Kawasaki-type  
dynamics in
the lattice without exclusion, and in the continuum. New estimates for
Glauber-type dynamics are also obtained.


http://front.math.ucdavis.edu/math.PR/0505533

---------------------------------------------------------------

3390. CONCENTRATION INEQUALITIES ON PRODUCT SPACES WITH APPLICATIONS  
TO MARKOV  PROCESSES

Gordon Blower and  Fran\c{c}ois Bolley (UMPA-ENSL)

For a stochastic process with state space some Polish space, this  
paper gives
sufficient conditions on the initial and conditional distributions  
for the
joint law to satisfy Gaussian concentration inequalities, transportation
inequalities and also logarithmic Sobolev inequalities in the case of  
the
Euclidean space. In several cases, the obtained constants are of  
optimal order
of growth with respect to the number of variables, or are independent  
of this
number. These results extend results known for mutually independent  
variables
to weakly dependent variables under Dobrushin-Shlosman type conditions.


http://front.math.ucdavis.edu/math.PR/0505536

---------------------------------------------------------------

3391. DE BRUIJN COVERING CODES FOR ROOTED HYPERGRAPHS

Joshua N. Cooper and  Fan Chung

What is the length of the shortest sequence $S$ of reals so that the  
set of
consecutive $n$-words in $S$ form a covering code for permutations on  
$\{1,2,
 >..., n\}$ of radius $R$ ? (The distance between two $n$-words is  
the number of
transpositions needed to have the same order type.) The above problem  
can be
viewed as a special case of finding a De Bruijn covering code for a  
rooted
hypergraph. Each edge of a rooted hypergraph contains a special  
vertex, called
the {\it root} of the edge, and each vertex is the root of a unique  
edge,
called its {\it ball}. A De Bruijn covering code is a subset of the  
roots such
that every vertex is in some edge containing a chosen root. Under  
some mild
conditions, we obtain an upper bound for the shortest length of a De  
Bruijn
covering code of a rooted hypergraph, a bound which is within a  
factor of $\log
n$ of the lower bound.


http://front.math.ucdavis.edu/math.CO/0505528

---------------------------------------------------------------

3392. RANDOM GROWTH MODELS WITH POLYGONAL SHAPES

Janko Gravner and  David Griffeath

We consider discrete time random perturbations of monotone cellular  
automata
(CA) in two dimensions. Under general conditions, we prove the  
existence of
half--space velocities, and then establish the validity of the Wulff
construction for asymptotic shapes arising from finite initial seeds.  
Such a
shape converges to the polygonal invariant shape of the corresponding
deterministic model as the perturbation decreases. In many cases, exact
stability is observed. That is, for small perturbations, the shapes  
of the
deterministic and random processes agree exactly. We give a complete
characterization of such cases, and show that they are prevalent among
threshold growth CA with box neighborhood. We also design a  
nontrivial family
of CA in which the shape is exactly computable for all values of its
probability parameter.


http://front.math.ucdavis.edu/math.PR/0505039

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3393. STOCHASTIC DIFFERENTIAL EQUATIONS DRIVEN BY PURELY SPATIAL NOISE

S. V. Lototsky and  B. L. Rozovskii

Space-only noise is a natural random perturbation in equations  
without time
evolution. Even the simplest equations driven by this noise often do  
not have a
square-integrable solution and must be solved in special weighted  
spaces. The
Cameron-Martin version of the Wiener chaos decomposition is an  
effective tool
to study both stationary and evolution equations driven by space-only  
noise.
The paper presents the main results about solvability of such  
equations in
weighted Wiener chaos spaces and studies the long-time behavior of the
solutions of evolution equations with space-only noise.


http://front.math.ucdavis.edu/math.PR/0505551

---------------------------------------------------------------

3394. JACOBIANS AND RANK 1 PERTURBATIONS RELATING TO UNITARY  
HESSENBERG  MATRICES

Peter J. Forrester and Eric M. Rains

In a recent work Killip and Nenciu gave random recurrences for the
characteristic polynomials of certain unitary and real orthogonal upper
Hessenberg matrices. The corresponding eigenvalue p.d.f.'s are
beta-generalizations of the classical groups. Left open was the direct
calculation of certain Jacobians. We provide the sought direct  
calculation.
Furthermore, we show how a multiplicative rank 1 perturbation of the  
unitary
Hessenberg matrices provides a joint eigenvalue p.d.f generalizing  
the circular
beta-ensemble, and we show how this joint density is related to known
inter-relations between circular ensembles. Projecting the joint  
density onto
the real line leads to the derivation of a random three-term  
recurrence for
polynomials with zeros distributed according to the circular Jacobi
beta-ensemble.


http://front.math.ucdavis.edu/math.PR/0505552

---------------------------------------------------------------

3395. ON RANDOM MEASURES ON THE SPACE OF TRAJECTORIES AND STRONG AND  
WEAK  SOLUTIONS OF STOCHASTIC EQUATIONS

A. A. Dorogovtsev

The random measures on the space of continuous functions are considered.
Stationary random measures are described. The weak solutions of the  
stochastic
equations are substituted by the strong measure-valued solutions.


http://front.math.ucdavis.edu/math.PR/0505569

---------------------------------------------------------------

3396. ASYMPTOTIC BEHAVIOR OF THE NUMBER OF LOST MESSAGES

Vyacheslav M. Abramov

The goal of the paper is to study asymptotic behavior of the number  
of lost
messages. Long messages are assumed to be divided into a random  
number of
packets which are transmitted independently of one another. An error in
transmission of a packet results in the loss of the entire message.  
Messages
arrive to the $M/GI/1$ finite buffer model and can be lost in two  
cases as
either at least one of its packets is corrupted or the buffer is  
overflowed.
With the parameters of the system typical for models of information
transmission in real networks, we obtain theorems on asymptotic  
behavior of the
number of lost messages. We also study how the loss probability  
changes if
redundant packets are added. Our asymptotic analysis approach is  
based on
Tauberian theorems with remainder.


http://front.math.ucdavis.edu/math.PR/0505596

---------------------------------------------------------------

3397. ASYMPTOTIC ANALYSIS OF THE GI/M/1/N LOSS SYSTEM AS N INCREASES  
TO  INFINITY

Vyacheslav M. Abramov

This paper provides the asymptotic analysis of the loss probability  
in the
$GI/M/1/n$ queueing system as $n$ increases to infinity. The approach  
of this
paper is alternative to that of the recent papers of Choi and Kim  
[2000] and
Choi et al [2000] and based on application of modern Tauberian  
theorems with
remainder. This enables us to simplify the proofs of the results on  
asymptotic
behavior of the loss probability of the abovementioned paper of Choi  
and Kim
[2000] as well as to obtain some new results.


http://front.math.ucdavis.edu/math.PR/0505597

---------------------------------------------------------------

3398. STOCHASTIC GAMES WITH INFINITELY MANY INTERACTING AGENTS

Emilio De Santis and Carlo Marinelli

We introduce and study a class of infinite-horizon non-zero-sum
non-cooperative stochastic games with infinitely many interacting  
agents using
ideas of statistical mechanics. First we show, in the general case of
asymmetric interactions, the existence of a strategy that allows any  
player to
eliminate losses after a finite random time. In the special case of  
symmetric
interactions, we also prove that, as time goes to infinity, the game  
converges
to a Nash equilibrium. Moreover, assuming that all agents adopt the same
strategy, using arguments related to those leading to perfect simulation
algorithms, spatial mixing and ergodicity are proved. In turn,  
ergodicity
allows us to prove ``fixation'', i.e. that players will adopt a constant
strategy after a finite time. The resulting dynamics is related to
zero-temperature Glauber dynamics on random graphs of possibly  
infinite volume.


http://front.math.ucdavis.edu/math.PR/0505608

---------------------------------------------------------------

3399. THE STABILITY OF JOIN-THE-SHORTEST-QUEUE MODELS WITH GENERAL  
INPUT AND  OUTPUT PROCESSES

Vyacheslav M. Abramov

The paper establishes necessary and sufficient conditions for the  
stability
of different join-the-shortest-queue models including the load- 
balanced network
with general input and output processes. It is shown that the  
necessary and
sufficient condition for the stability of the load-balanced network  
is related
to the solution of the linear programming problem precisely  
formulated in the
paper. It is proved that if the minimum of the objective function of  
that
linear programming problem is less than 1, then the associated load- 
balanced
network is stable.


http://front.math.ucdavis.edu/math.PR/0505040

---------------------------------------------------------------

3400. LONG RANGE ACTION IN NETWORKS OF CHAOTIC ELEMENTS

Michael Blank and  Leonid Bunimovich

We show that under certain simple assumptions on the topology  
(structure) of
networks of strongly interacting chaotic elements a phenomenon of  
long range
action takes place, namely that the asymptotic (as time goes to  
infinity)
dynamics of an arbitrary large network is completely determined by  
its boundary
conditions. This phenomenon takes place under very mild and robust  
assumptions
on local dynamics with short range interactions. However, we show  
that it is
unstable with respect to arbitrarily weak local random perturbations.


http://front.math.ucdavis.edu/math.DS/0505610

---------------------------------------------------------------

3401. ANALYSIS OF MULTISERVER RETRIAL QUEUEING SYSTEM: A MARTINGALE  
APPROACH  AND AN ALGORITHM OF SOLUTION

Vyacheslav M. Abramov

The paper studies a multiserver retrial queueing system with $m$  
servers.
Arrival process is a point process with strictly stationary and ergodic
increments. A customer arriving to the system occupies one of the  
free servers.
If upon arrival all servers are busy, then the customer goes to the  
secondary
queue, orbit, and after some random time retries more and more to  
occupy a
server. A service time of each customer is exponentially distributed  
random
variable with parameter $\mu_1$. A time between retrials is  
exponentially
distributed with parameter $\mu_2$ for each customer. Using a martingale
approach the paper provides an analysis of this system. The paper  
establishes
the stability condition and studies a behavior of the limiting queue- 
length
distributions as $\mu_2$ increases to infinity. As $\mu_2\to\infty$,  
the paper
also proves the convergence of appropriate queue-length distributions  
to those
of the associated `usual' multiserver queueing system without  
retrials. An
algorithm for numerical solution of the equations, associated with  
the limiting
queue-length distribution of retrial systems, is provided.


http://front.math.ucdavis.edu/math.PR/0505046

---------------------------------------------------------------

3402. THE CENTRAL LIMIT PROBLEM FOR RANDOM VECTORS WITH SYMMETRIES

Elizabeth S. Meckes and  Mark W. Meckes

Motivated by the central limit problem for convex bodies, we study  
normal
approximation of linear functionals of high-dimensional random  
vectors with
various types of symmetries. In particular, we obtain results for  
distributions
which are coordinatewise symmetric, uniform in a regular simplex, or
spherically symmetric. Our proofs are based on Stein's method of  
exchangeable
pairs; as far as we know, this approach has not previously been used  
in convex
geometry and we give a brief introduction to the classical method. The
spherically symmetric case is treated by a variation of Stein's  
method which is
adapted for continuous symmetries.


http://front.math.ucdavis.edu/math.PR/0505618

---------------------------------------------------------------

3403. A CLASS OF REMARKABLE SUBMARTINGALES (II): ENLARGEMENTS OF  
FILTRATIONS

Ashkan Nikeghbali

Az\'{e}ma associated with an honest time $L$ the supermartingale
$Z_{t}^{L}=\mathbb{P}[L>t|\mathcal{F}_{t}]$ and established some of its
important properties. This supermartingale plays a central role in  
the general
theory of stochastic processes and in particular in the theory of  
progressive
enlargements of filtrations. In this paper, we shall give an additive
characterization for these supermartingales, which in turn will  
naturally
provide many examples of enlargements of filtrations. In particular,  
we use
this characterization to establish some path decomposition results,  
closely
related to or reminiscent of Williams' path decomposition results.


http://front.math.ucdavis.edu/math.PR/0505623

---------------------------------------------------------------

3404. ON THE SPATIAL MEAN OF THE POINCARE CYCLE

Luis Baez-Duarte

Let $X$ be a measure space and $T:X\to X$ a measurable  
transformation. For
any measurable $E\subseteq X$ and $x\in E$, the possibly infinite  
return time
is $n_E(x):=\inf\{n>0: T^n x\in E\}$. If $T$ is an ergodic  
tranformation of the
probability space $X$, and $\mu(E)>0$, then a theorem of M. Kac  
states that
$\int_E n_E d\mu=1$. We generalize this to any invertible measure  
preserving
transformation $T$ on a finite measure space $X$, by proving  
independently, and
nearly trivially that for any measurable $E\subseteq X$ one has $ 
\int_E n_E
d\mu=\mu(I_E)$, where $I_E$ is the smallest invariant set containing  
$E$. In
particular this also provides a simpler proof of Poincar\'{e}'s  
recurrence
theorem.


http://front.math.ucdavis.edu/math.PR/0505625

---------------------------------------------------------------

3405. POISSON MICROBALLS: SELF-SIMILARITY AND DIRECTIONAL ANALYSIS

Hermine Bierm\'e and Anne Estrade

We study a random field obtained by counting the number of balls  
containing
each point, when overlapping balls are thrown at random according to  
a Poisson
random measure. We are particularly interested in the local asymptotical
self-similarity (lass) properties of the field, as well as the action  
of X-ray
transforms. We exhibit two different lass properties when considering  
the
asymptotic either "in law" or "on the second order moment" and prove a
relationship between the lass behavior of the field and the lass  
behavior of
its X-ray transform. These results can be exploited to modelize and  
analyze
granular media, images or connections network.


http://front.math.ucdavis.edu/math.PR/0505635

---------------------------------------------------------------

3406. EQUILIBRIUM FLUCTUATIONS FOR A ONE-DIMENSIONAL INTERFACE IN THE  
SOLID ON  SOLID APPROXIMATION

Gustavo Posta

An unbounded one-dimensional solid-on-solid model with integer  
heights is
studied. Unbounded here means that there is no a priori restrictions  
on the
discret e gradient of the interface. The interaction Hamiltonian of the
interface is given by a finite range part, pr oportional to the sum  
of height
differences, plus a part of exponentially decaying long range  
potentials. The
evolution of the interface is a reversible Markov process. We prove  
that if
this system is started in the center of a box of size L after a time  
of order
L^3 it reaches, with a very large probability, the top or the bottom  
of the
box.


http://front.math.ucdavis.edu/math.PR/0505643

---------------------------------------------------------------

3407. INFLUENCE AND SHARP-THRESHOLD THEOREMS FOR MONOTONIC MEASURES

B. T. Graham and G. R. Grimmett

The influence theorem for product measures on the discrete space {0,1} 
^N may
be extended to probability measures with the property of monotonicity  
(which is
equivalent to `strong positive-association'). Corresponding results  
are valid
for probability measures on the cube [0,1]^N that are absolutely  
continuous
with respect to Lebesgue measure. These results lead to a sharp- 
threshold
theorem for measures of random-cluster type, and this may be applied to
box-crossings in the two-dimensional random-cluster model.


http://front.math.ucdavis.edu/math.PR/0505057

---------------------------------------------------------------

3408. THE STOCHASTIC ACCELERATION PROBLEM IN TWO DIMENSIONS

T. Komorowski and L. Ryzhik

We consider the motion of a particle in a two-dimensional spatially
homogeneous mixing potential and show that its momentum converges to the
Brownian motion on a circle. This complements the limit theorem of  
Kesten and
Papanicolaou \cite{KP} proved in dimensions $d\ge 3$.


http://front.math.ucdavis.edu/math-ph/0505083

---------------------------------------------------------------

3409. ON THE PERIODIC PROPERTIES OF SELF-DECIMATED GENERATORS OF  
PSEUDORANDOM  NUMBERS

Sergey Agievich and  Oleg Solovey

We consider a self-decimated generator of pseudorandom numbers and  
examine
the preperiod $\lambda$ and the period $\mu$ of its state sequence.  
We obtain
the expectations and variances of $\lambda$ and $\mu$ for the case when
decimation steps are chosen randomly and independently from the set  
{1,2}.


http://front.math.ucdavis.edu/math.CO/0505660

---------------------------------------------------------------

3410. NEW SCALING OF ITZYKSON-ZUBER INTEGRALS

Benoit Collins and  Piotr Sniady

We study asymptotics of the Itzykson-Zuber integrals in the scaling  
when one
of the matrices has a small rank compared to the full rank. We show  
that the
result is basically the same as in the case when one of the matrices  
has a
fixed rank. In this way we extend the recent results of Guionnet and  
Maida who
showed that for a latter scaling the Itzykson-Zuber integral is given  
in terms
of the Voiculescu's R-transform of the full rank matrix.


http://front.math.ucdavis.edu/math.PR/0505664

---------------------------------------------------------------

3411. A STABLE MARRIAGE OF POISSON AND LEBESGUE

Christopher Hoffman and  Alexander E. Holroyd and Yuval Peres

Let $\Xi$ be a discrete set in $\rd$. Call the elements of $\Xi$  
centers. The
well-known Voronoi tessellation partitions $\rd$ into polyhedral  
regions (of
varying sizes) by allocating each site of $\rd$ to the closest  
center. Here we
study "fair" allocations of $\rd$ to $\Xi$ in which the regions  
allocated to
different centers have equal volumes.
   We prove that if $\Xi$ is obtained from a translation-invariant  
ergodic point
process, then there is a unique fair allocation which is stable in  
the sense of
the Gale-Shapley marriage problem. (That is, sites and centers both  
prefer to
be allocated as close as possible, and an allocation is said to be  
unstable if
some site and center both prefer each other over their current  
allocations.)
   We show that the region allocated to each center $\xi$ is a union  
of finitely
many bounded connected sets. However, in the case of a Poisson  
process, an
infinite volume of sites are allocated to a centers further away than  
$\xi$. We
prove power law lower bounds on the allocation distance of a typical  
site. It
is an open problem to prove any upper bound in $d>1$.


http://front.math.ucdavis.edu/math.PR/0505668

---------------------------------------------------------------

3412. ON CONVERGENCE OF IMPORTANCE SAMPLING AND OTHER PROPERLY  
WEIGHTED  SAMPLES TO THE TARGET DISTRIBUTION

S. Malefaki and  G. Iliopoulos

We consider importance sampling as well as other properly weighted  
samples
with respect to a target distribution $\pi$ from a different point of  
view. By
considering the associated weights as sojourn times until the next  
jump, we
define appropriate jump processes. When the original sample sequence  
forms an
ergodic Markov chain, the associated jump process is an ergodic semi-- 
Markov
process with stationary distribution $\pi$. Hence, the type of  
convergence of
properly weighted samples may be stronger than that of weighted  
means. In
particular, when the samples are independent and the mean weight is  
bounded
above, we describe a slight modification in order to achieve exact  
(weighted)
samples from the target distribution.


http://front.math.ucdavis.edu/math.ST/0505045

---------------------------------------------------------------

3413. QUENCHED INVARIANCE PRINCIPLES FOR RANDOM WALKS ON PERCOLATION  
CLUSTERS

P. Mathieu and A. L. Piatnitski

We prove the almost sure ('quenched') invariance principle for a random
walker on an infinite Bernoulli percolation cluster in $\Z^d$ where $d 
$ is
larger or equal than 2.


http://front.math.ucdavis.edu/math.PR/0505672

---------------------------------------------------------------

3414. RIGOROUS RESULTS ON THE THRESHOLD NETWORK MODEL

Norio Konno and  Naoki Masuda and  Rahul Roy and  Anish Sarkar

We analyze the threshold network model in which a pair of vertices with
random weights are connected by an edge when the summation of the  
weights
exceeds a threshold. We prove some convergence theorems and central  
limit
theorems on the vertex degree, degree correlation, and the number of  
prescribed
subgraphs. We also generalize some results in the spatially extended  
cases.


http://front.math.ucdavis.edu/math.PR/0505681

---------------------------------------------------------------

3415. LOWER DEVIATION PROBABILITIES FOR SUPERCRITICAL GALTON-WATSON  
PROCESSES

Klaus Fleischmann and Vitali Wachtel

There is a well-known sequence of constants c_n describing the growth of
supercritical Galton-Watson processes Z_n. With 'lower deviation  
probabilities'
we refer to P(Z_n=k_n) with k_n=o(c_n) as n increases. We give a  
detailed
picture of the asymptotic behavior of such lower deviation  
probabilities. This
complements and corrects results known from the literature concerning  
special
cases. Knowledge on lower deviation probabilities is needed to  
describe large
deviations of the ratio Z_{n+1}/Z_n. The latter are important in  
statistical
inference to estimate the offspring mean. For our proofs, we adapt the
well-known Cramer method for proving large deviations of sums of  
independent
variables to our needs.


http://front.math.ucdavis.edu/math.PR/0505683

---------------------------------------------------------------

3416. DELAY DIFFERENTIAL EQUATIONS DRIVEN BY LEVY PROCESSES:  
STATIONARITY AND  FELLER PROPERTIES

M. Reiss and  M. Riedle and  O. van Gaans

We consider a stochastic delay differential equation driven by a  
general Levy
process. Both, the drift and the noise term may depend on the past,  
but only
the drift term is assumed to be linear. We show that the segment  
process is
eventually Feller, but in general not eventually strong Feller on the  
Skorokhod
space. The existence of an invariant measure is shown by proving  
tightness of
the segments using semimartingale characteristics and the Krylov- 
Bogoliubov
method. A counterexample shows that the stationary solution in  
completely
general situations may not be unique, but in more specific cases  
uniqueness is
established.


http://front.math.ucdavis.edu/math.PR/0505684

---------------------------------------------------------------

3417. SELF-SIMILAR AND MARKOV COMPOSITION STRUCTURES

Alexander Gnedin and Jim Pitman

The bijection between composition structures and random closed  
subsets of the
unit interval implies that the composition structures associated with  
$S \cap
[0,1]$ for a self-similar random set $S\subset {\mathbb R}_+$ are  
those which
are consistent with respect to a simple truncation operation. Using the
standard coding of compositions by finite strings of binary digits  
starting
with a 1, the random composition of $n$ is defined by the first $n$  
terms of a
random binary sequence of infinite length. The locations of 1s in the  
sequence
are the places visited by an increasing time-homogeneous Markov chain  
on the
positive integers if and only if $S = \exp(-W)$ for some stationary
regenerative random subset $W$ of the real line. Complementing our  
study in
previous papers, we identify self-similar Markovian composition  
structures
associated with the two-parameter family of partition structures.


http://front.math.ucdavis.edu/math.PR/0505687

---------------------------------------------------------------

3418. MIXING TIME BOUNDS VIA THE SPECTRAL PROFILE

Sharad Goel and  Ravi Montenegro and  Prasad Tetali

On complete, non-compact manifolds and infinite graphs, Faber-Krahn
inequalities have been used to estimate the rate of decay of the heat  
kernel.
We develop this technique in the setting of finite Markov chains,  
proving upper
and lower mixing time bounds via the spectral profile. This approach  
lets us
recover and refine previous conductance-based bounds of mixing time  
(including
the Morris-Peres result), and in general leads to sharper estimates of
convergence rates. We apply this method to several models including  
groups with
moderate growth, the fractal-like Viscek graphs, and the torus, to  
obtain tight
bounds on the corresponding mixing times.


http://front.math.ucdavis.edu/math.PR/0505690

---------------------------------------------------------------

3419. RANK INDEPENDENCE AND REARRANGEMENTS OF RANDOM VARIABLES

Alexander Gnedin and Zbigniew Nitecki

A rearrangement of $n$ independent uniform $[0,1]$ random variables is a
sequence of $n$ random variables $Y_1,...,Y_n$ whose vector of order  
statistics
has the same distribution as that for the $n$ uniforms. We consider
rearrangements satisfying the strong rank independence condition,  
that the rank
of $Y_k$ among $Y_1,...,Y_k$ is independent of the values of  
$Y_1,...,Y_{k-1}$,
for $k=1,...,n$. Nontrivial examples of such rearrangements are the  
travellers'
processes defined by Gnedin and Krengel. We show that these are the only
examples when $n=2$, and when certain restrictive assumptions hold  
for $n\geq
3$; we also construct a new class of examples of such rearrangements  
for which
the restrictive assumptions do not hold.


http://front.math.ucdavis.edu/math.PR/0505692

---------------------------------------------------------------

3420. EFFICIENT SPIKE-SORTING OF MULTI-STATE NEURONS USING INTER- 
SPIKE  INTERVALS INFORMATION

Matthieu Delescluse (LPC) and  Christophe Pouzat (LPC)

We demonstrate the efficacy of a new spike-sorting method based on a  
Markov
Chain Monte Carlo (MCMC) algorithm by applying it to real data  
recorded from
Purkinje cells (PCs) in young rat cerebellar slices. This algorithm  
is unique
in its capability to estimate and make use of the firing statistics  
as well as
the spike amplitude dynamics of the recorded neurons. PCs exhibit  
multiple
discharge states, giving rise to multimodal interspike interval (ISI)
histograms and to correlations between successive ISIs. The amplitude  
of the
spikes generated by a PC in an "active" state decreases, a feature  
typical of
many neurons from both vertebrates and invertebrates. These two features
constitute a major and recurrent problem for all the presently available
spike-sorting methods. We first show that a Hidden Markov Model with 3
log-Normal states provides a flexible and satisfying description of  
the complex
firing of single PCs. We then incorporate this model into our  
previous MCMC
based spike-sorting algorithm (Pouzat et al, 2004, J. Neurophys. 91,  
2910-2928)
and test this new algorithm on multi-unit recordings of bursting PCs.  
We show
that our method successfully classifies the bursty spike trains fired  
by PCs by
using an independent single unit recording from a patch-clamp pipette.


http://front.math.ucdavis.edu/q-bio.QM/0505053

---------------------------------------------------------------

3421. HYDRODYNAMIC SCALING LIMIT OF CONTINUUM SOLID-ON-SOLID MODEL

Anamaria Savu

A fourth-order nonlinear evolution equation is derived from a  
microscopic
model for surface diffusion, namely, the continuum solid-on-solid  
model. We use
the method developed by Varadhan for the computation of hydrodynamic  
scaling
limit of nongradient models. What distinguishes our model from other  
models
discussed so far is the presence of two conservation laws for the  
dynamics in a
nonperiodic box and the complex dynamics that is not nearest- 
neighbor. Along
the way, a few steps has to be adapted to our new context. As a  
byproduct of
our main result we also derive the hydrodynamic scaling limit of a  
perturbation
of continuum solid-on-solid model, a model that incorporates both  
surface
diffusion and surface electromigration.


http://front.math.ucdavis.edu/math.PR/0506001

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3422. ASYMPTOTIC STATISTICAL EQUIVALENCE FOR ERGODIC DIFFUSIONS: THE   
MULTIDIMENSIONAL CASE

Arnak Dalalyan (PMA) and  Markus Reiss (WIAS)

Asymptotic local equivalence in the sense of Le Cam is established for
inference on the drift in multidimensional ergodic diffusions and an
accompanying sequence of Gaussian shift experiments. The  
nonparametric local
neighbourhoods can be attained for any dimension, provided the  
regularity of
the drift is sufficiently large. In addition, a heteroskedastic Gaussian
regression experiment is given, which is also locally asymptotically  
equivalent
and which does not depend on the centre of localisation. For one  
direction of
the equivalence an explicit Markov kernel is constructed.


http://front.math.ucdavis.edu/math.ST/0505053

---------------------------------------------------------------

3423. A CHARACTERIZATION OF MARKOV PROCESSES ENJOYING THE TIME- 
INVERSION  PROPERTY

Stephan Lawi

We give a necessary and sufficient condition for a homogeneous Markov  
process
taking values in $\R^n$ to enjoy the time-inversion property of degree
$\alpha$. The condition sets the shape for the semigroup densities of  
the
process and allows to further extend the class of known processes  
satisfying
the time-inversion property. As an application we recover the result of
Watanabe in \cite{Wa1975} for continuous and conservative Markov  
processes on
$\R_+$. As new examples we generalize Dunkl processes and construct a
matrix-valued process with jumps related to the Wishart process by a
skew-product representation.


http://front.math.ucdavis.edu/math.PR/0506013

---------------------------------------------------------------

3424. CLOSED AND EXACT FUNCTIONS IN THE CONTEXT OF GINZBURG-LANDAU  
MODELS

Anamaria Savu

For a general vector field we exhibit two Hilbert spaces, namely the  
space of
so called closed functions and the space of exact functions and we  
calculate
the codimension of the space of exact functions inside the larger  
space of
closed functions. In particular we provide a new approach for the  
known cases:
the Glauber field and the second-order Ginzburg-Landau field, and for  
the case
of the fourth-order Ginzburg-Landau field.


http://front.math.ucdavis.edu/math.FA/0506002

---------------------------------------------------------------

3425. MOMENT INEQUALITIES FOR U-STATISTICS

Radoslaw Adamczak

We present moment inequalities for completely degenerate Banach space  
valued
(generalized) U-statistics of arbitrary order. The estimates involve  
suprema of
empirical processes, which in the real valued case can be replaced by  
simpler
norms of the kernel matrix (i.e. norms of some multilinear operators  
associated
with the kernel matrix). As a corollary we derive tail inequalities for
U-statistics with bounded kernels and for some multiple stochastic  
integrals.


http://front.math.ucdavis.edu/math.PR/0506026

---------------------------------------------------------------

3426. LOSSES IN M/GI/M/N QUEUES

Vyacheslav M. Abramov

The $M/GI/m/n$ queueing system under the assumption that $\lambda = m 
\mu$ is
considered, where $\lambda$ is the rate of arrivals, $\mu$ is the  
reciprocal of
the expected service times, $m$ is the number of servers and $n$ is the
maximally possible queue-length. It is proved that the expectation of  
the
number of losses during a busy period is equal to $m^m/m!$ for all $n 
\geq 0$.
This result is an extension of the corresponding result for the $M/GI/ 
1/n$
queueing system established originally by the author.


http://front.math.ucdavis.edu/math.PR/0506033

---------------------------------------------------------------

3427. DYNAMICS AND ENDOGENY FOR RECURSIVE PROCESSES ON TREES

Jon Warren

We consider stochastic processes indexed by the vertices of an infinite
binary tree having a simple recursive structure. The value at any  
vertex is
some fixed function of the values at the two daughter vertices  
together with
some independent innovation. Endogeny means the innovations are  
generating.
When endogeny does not hold there exist dynamics in which the  
innovations are
held fixed while some additional randomness on the boundary of the  
tree is
perturbed.


http://front.math.ucdavis.edu/math.PR/0506038

---------------------------------------------------------------

3428. A UNIFYING CLASS OF SKOROKHOD EMBEDDINGS: CONNECTING THE AZEMA- 
YOR AND  VALLOIS EMBEDDINGS

A. M. G. Cox and  D. G. Hobson

In this paper we consider the Skorokhod embedding problem in Brownian  
motion.
In particular, we give a solution based on the local time at zero of  
a variably
skewed Brownian motion related to the underlying Brownian motion.  
Special cases
of the construction include the Azema-Yor and Vallois embeddings. In  
turn, the
construction has an interpretation in the Chacon-Walsh framework.


http://front.math.ucdavis.edu/math.PR/0506040

---------------------------------------------------------------

3429. FREE-DIFFERENTIABILITY CONDITIONS ON THE FREE-ENERGY FUNCTION  
IMPLYING  LARGE DEVIATIONS

Henri Comman

Let $(\mu_{\alpha})$ be a net of Radon sub-probability measures on  
the real
line, and $(t_{\alpha})$ be a net in $]0,+\infty[$ converging to 0.  
Assuming
that the generalized log-moment generating function $L(\lambda)$  
exists for all
$\lambda$ in a nonempty open interval $G$, we give conditions on the  
left or
right derivatives of $L_{\mid G}$, implying vague (and thus narrow  
when $0\in
G$) large deviations. The rate function (which can be nonconvex) is  
obtained as
an abstract Legendre-Fenchel transform. This allows us to strengthen the
G\"{a}rtner-Ellis theorem by removing the usual differentiability  
assumption. A
related question of R. S. Ellis is solved.


http://front.math.ucdavis.edu/math.PR/0506044

---------------------------------------------------------------

3430. DIFFUSING POLYGONS AND SLE($\KAPPA,\RHO$)

Robert O. Bauer and  Roland M. Friedrich

We give a geometric derivation of SLE($\kappa,\rho$) in terms of  
conformally
invariant random growing subsets of polygons. We relate the  
parameters $\rho_j$
to the exterior angles of the polygons. We also show that SLE($\kappa, 
\rho$)
can be generated by a metric Brownian motion, where metric and  
Brownian motion
are coupled and the metric ist the pull-back metric of the Euclidean  
metric of
an evolving polygon.


http://front.math.ucdavis.edu/math.PR/0506062

---------------------------------------------------------------

3431. STUDY ON OPTIMAL TIMING OF MARK-TO-MARKET FOR CONTINGENT CREDIT  
RISK  CONTROL

Jiali Liao and Ted Theodosopoulos

Over-the-counter derivatives have contributed significantly to the
effectiveness and efficiency of the international financial system  
but also
entail significant counterparty credit risk. Collateralization is one  
of the
most important and widespread credit risk mitigation techniques used in
derivatives transactions. However, the relevant decisions are often  
made in an
ad-hoc manner, without reference to an analytical framework. Very little
academic research has addressed the quantitative analysis of  
collateralization
for contingent credit risk control. The issue of mark-to-market  
timing becomes
important for reducing credit exposure of illiquid and long term  
derivative
contracts due to the difficulty and cost of marking to market. the  
goal of this
research is to propose a framework for minimizing the potential  
credit exposure
of collateralized derivative transactions by optimizing mark-to- 
market timing.


http://front.math.ucdavis.edu/math.PR/0506077

---------------------------------------------------------------

3432. STOCHASTIC FLOWS ASSOCIATED TO COALESCENT PROCESSES III: LIMIT  
THEOREMS

Jean Bertoin (PMA) and  Jean-Fran\c{c}ois Le Gall (DMA)

We prove several limit theorems that relate coalescent processes to
continuous-state branching processes. Some of these theorems are  
stated in
terms of the so-called generalized Fleming-Viot processes, which  
describe the
evolution of a population with fixed size, and are duals to the  
coalescents
with multiple collisions studied by Pitman and others. We first discuss
asymptotics when the initial size of the population tends to  
infinity. In that
setting, under appropriate hypotheses, we show that a rescaled  
version of the
generalized Fleming-Viot process converges weakly to a continuous-state
branching process. As a corollary, we get a hydrodynamic limit for  
certain
sequences of coalescents with multiple collisions: Under an appropriate
scaling, the empirical measure associated with sizes of the blocks  
converges to
a (deterministic) limit which solves a generalized form of  
Smoluchowski's
coagulation equation. We also study the behavior in small time of a  
fixed
coalescent with multiple collisions, under a regular variation  
assumption on
the tail of the measure $\nu$ governing the coalescence events.  
Precisely, we
prove that the number of blocks with size less than $\epsilon x$ at time
$(\epsilon\nu([\epsilon,1]))^{-1}$ behaves like
$\epsilon^{-1}\lambda\_1(]0,x[)$ as $\epsilon\to 0$, where $\lambda\_1 
$ is the
distribution of the size of one cluster at time 1 in a continuous-state
branching process with stable branching mechanism. This generalizes a  
classical
result for the Kingman coalescent.


http://front.math.ucdavis.edu/math.PR/0506092

---------------------------------------------------------------

3433. TWO NEW MARKOV ORDER ESTIMATORS

Yuval Peres and Paul Shields

We present two new methods for estimating the order (memory depth) of a
finite alphabet Markov chain from observation of a sample path. One  
method is
based on entropy estimation via recurrence times of patterns, and the  
other
relies on a comparison of empirical conditional probabilities. The  
key to both
methods is a qualitative change that occurs when a parameter (a  
candidate for
the order) passes the true order. We also present extensions to order
estimation for Markov random fields.


http://front.math.ucdavis.edu/math.ST/0506080

---------------------------------------------------------------

3434. DIFFUSION MAPS, SPECTRAL CLUSTERING AND EIGENFUNCTIONS OF  
FOKKER-PLANCK  OPERATORS

Boaz Nadler and  Stephane Lafon and  Ronald R. Coifman and  Ioannis  
G. Kevrekidis

This paper presents a diffusion based probabilistic interpretation of
spectral clustering and dimensionality reduction algorithms that use the
eigenvectors of the normalized graph Laplacian. Given the pairwise  
adjacency
matrix of all points, we define a diffusion distance between any two  
data
points and show that the low dimensional representation of the data  
by the
first few eigenvectors of the corresponding Markov matrix is optimal  
under a
certain mean squared error criterion. Furthermore, assuming that data  
points
are random samples from a density $p(\x) = e^{-U(\x)}$ we identify these
eigenvectors as discrete approximations of eigenfunctions of a Fokker- 
Planck
operator in a potential $2U(\x)$ with reflecting boundary conditions.  
Finally,
applying known results regarding the eigenvalues and eigenfunctions  
of the
continuous Fokker-Planck operator, we provide a mathematical  
justification for
the success of spectral clustering and dimensional reduction  
algorithms based
on these first few eigenvectors. This analysis elucidates, in terms  
of the
characteristics of diffusion processes, many empirical findings  
regarding
spectral clustering algorithms.


http://front.math.ucdavis.edu/math.NA/0506090

---------------------------------------------------------------

3435. A NOTE ON THE RUIN PROBLEM WITH RISKY INVESTMENTS

David Maher

We reprove a result concerning certain ruin in the classical problem  
of the
probability of ruin with risky investments and several of it's  
generalisations.
We also provide the combined transition density of the risk and  
investment
processes in the diffusion case.


http://front.math.ucdavis.edu/math.PR/0506127

---------------------------------------------------------------

3436. RATE OF ESCAPE OF THE MIXER CHAIN

Ariel Yadin

We study a Markov chain called the mixer chain, swapping tiles placed  
on a
graph. If the graph is a Cayley graph, this process is a random walk  
on a
semidirect product of groups. For the graph Z, we study the rate of  
escape of
this chain. We show that, with probability tending to 1 as time tends to
infinity, the chain is at distance at least t^{3/4} from its origin,  
and at
most t^{3/4} log^{5/4}(t).


http://front.math.ucdavis.edu/math.PR/0506129

---------------------------------------------------------------

3437. CONTINUOUS AND TRACTABLE MODELS FOR THE VARIATION OF  
EVOLUTIONARY RATES

Thomas Lepage (1) and  Stephan Lawi (2) and  Paul Tupper (1) and   
David Bryant (1)  ((1) McGill University (2) Universit\'e Pierre et  
Marie Curie)

We propose a continuous model for evolutionary rate variation across  
sites
and over the tree and derive exact transition probabilities under  
this model.
Changes in rate are modelled using the CIR process, a diffusion  
widely used in
financial applications. The model directly extends the standard gamma
distributed rates across site model, with one additional parameter  
governing
changes in rate down the tree. The parameters of the model can be  
estimated
directly from two well-known statistics: the index of dispersion and  
the gamma
shape parameter of the rates across sites model. The CIR model can be  
readily
incorporated into probabilistic models for sequence evolution. We  
provide here
an exact formula for the likelihood of a three taxa tree. Larger  
trees can be
evaluated using Monte-Carlo methods.


http://front.math.ucdavis.edu/math.PR/0506145

---------------------------------------------------------------

3438. QUANTITATIVE NOISE SENSITIVITY AND EXCEPTIONAL TIMES FOR  
PERCOLATION

Oded Schramm and Jeffrey E. Steif

One goal of this paper is to prove that dynamical critical site  
percolation
on the planar triangular lattice has exceptional times at which  
percolation
occurs. In doing so, new quantitative noise sensitivity results for  
percolation
are obtained. The latter is based on a novel method for controlling the
  "level k" Fourier coefficients via the construction of a randomized  
algorithm
which looks at random bits, outputs the value of a particular  
function but
looks at any fixed input bit with low probability. We also obtain  
upper and
lower bounds on the Hausdorff dimension of the set of percolating  
times. We
then study the problem of exceptional times for certain "k-arm"  
events on
wedges and cones. As a corollary of this analysis, we prove, among other
things, that there are no times at which there are two infinite "white"
clusters, obtain an upper bound on the Hausdorff dimension of the set  
of times
at which there are both an infinite white cluster and an infinite  
black cluster
and prove that for dynamical critical bond percolation on the square  
grid there
are no exceptional times at which three disjoint infinite clusters  
are present.


http://front.math.ucdavis.edu/math.PR/0504586

---------------------------------------------------------------

3439. A CENTRAL LIMIT THEOREM FOR NON-OVERLAPPING RETURN TIMES

Oliver Johnson

Define the non-overlapping return time of a random process to be the  
number
of blocks that we wait before a particular block reappears. We prove  
a Central
Limit Theorem based on these return times. This result has  
applications to
entropy estimation, and to the problem of determining if digits have  
come from
an independent equidistribted sequence. In the case of an  
equidistributed
sequence, we use an argument based on negative association to prove  
convergence
under weaker conditions.


http://front.math.ucdavis.edu/math.PR/0506165

---------------------------------------------------------------

3440. PRECISE ASYMPTOTICS FOR A RANDOM WALKER'S MAXIMUM

Alain Comtet and Satya N. Majumdar

We consider a discrete time random walk in one dimension. At each  
time step
the walker jumps by a random distance, independent from step to step,  
drawn
from an arbitrary symmetric density function. We show that the expected
positive maximum E[M_n] of the walk up to n steps behaves  
asymptotically for
large n as, E[M_n]/\sigma=\sqrt{2n/\pi}+ \gamma +O(n^{-1/2}), where  
\sigma^2 is
the variance of the step lengths. While the leading \sqrt{n} behavior is
universal and easy to derive, the leading correction term turns out  
to be a
nontrivial constant \gamma. For the special case of uniform  
distribution over
[-1,1], Coffmann et. al. recently computed \gamma=-0.516068...by exactly
enumerating a lengthy double series. Here we present a closed exact  
formula for
\gamma valid for arbitrary symmetric distributions. We also  
demonstrate how
\gamma appears in the thermodynamic limit as the leading behavior of the
difference variable E[M_n]-E[|x_n|] where x_n is the position of the  
walker
after n steps. An application of these results to the equilibrium
thermodynamics of a Rouse polymer chain is pointed out. We also  
generalize our
results to L\'evy walks.


http://front.math.ucdavis.edu/cond-mat/0506195

---------------------------------------------------------------

3441. NON-COLLIDING SYSTEM OF BROWNIAN PARTICLES AS PFAFFIAN PROCESS

Makoto Katori

In the paper [7] we studied the temporally inhomogeneous system of
non-colliding Brownian motions and proved that multi-time correlation  
functions
are generally given by the quaternion determinants in the sense of  
Dyson and
Mehta. In this report we give another proof of the equivalent  
statement using
Fredholm determinant and Fredholm pfaffian, and claim that the  
present system
is a typical example of pfaffian processes.


http://front.math.ucdavis.edu/math.PR/0506186

---------------------------------------------------------------

3442. INFINITE SYSTEMS OF NON-COLLIDING GENERALIZED MEANDERS AND   
RIEMANN-LIOUVILLE DIFFERINTEGRALS

Makoto Katori and  Hideki Tanemura

Yor's generalized meander is a temporally inhomogeneous modification  
of the
$2(\nu+1)$-dimensional Bessel process with $\nu > -1$, in which the
inhomogeneity is indexed by $\kappa \in [0, 2(\nu+1))$. We introduce the
non-colliding particle systems of the generalized meanders and prove  
that they
are the Pfaffian processes, in the sense that any multitime correlation
function is given by a Pfaffian. In the infinite particle limit, we  
show that
the elements of matrix kernels of the obtained infinite Pfaffian  
processes are
generally expressed by the Riemann-Liouville differintegrals of  
functions
comprising the Bessel functions $J_{\nu}$ used in the fractional  
calculus,
where orders of differintegration are determined by $\nu-\kappa$. As  
special
cases of the two parameters $(\nu, \kappa)$, the present infinite  
systems
include the quaternion determinantal processes studied by Forrester,  
Nagao and
Honner and by Nagao, which exhibit the temporal transitions between the
universality classes of random matrix theory.


http://front.math.ucdavis.edu/math.PR/0506187

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3443. A VARIATIONAL PRINCIPLE IN THE DUAL PAIR OF REPRODUCING KERNEL  
HILBERT  SPACES AND AN APPLICATION

Hyun Jae Yoo

Given a positive definite, bounded linear operator $A$ on the Hilbert  
space
$\mathcal{H}_0:=l^2(E)$, we consider a reproducing kernel Hilbert space
$\mathcal{H}_+$ with a reproducing kernel $A(x,y)$. Here $E$ is any  
countable
set and $A(x,y)$, $x,y\in E$, is the representation of $A$ w.r.t. the  
usual
basis of $\mathcal{H}_0$. Imposing further conditions on the operator  
$A$, we
also consider another reproducing kernel Hilbert space $\mathcal{H}_- 
$ with a
kernel function $B(x,y)$, which is the representation of the inverse  
of $A$ in
a sense, so that $\mathcal{H}_-\supset\mathcal{H}_0\supset\mathcal{H}_+$
becomes a rigged Hilbert space. We investigate a relationship between  
the
ratios of determinants of some partial matrices related to $A$ and $B 
$ and the
suitable projections in $\mathcal{H}_-$ and $\mathcal{H}_+$. We also  
get a
variational principle on the limit ratios of these values. We apply this
relation to show the Gibbsianness of the determinantal point process (or
fermion point process) defined by the operator $A(I+A)^{-1}$ on the  
set $E$. It
turns out that the class of determinantal point processes that can be
recognized as Gibbs measures for suitable interactions is much bigger  
than that
obtained by Shirai and Takahashi.


http://front.math.ucdavis.edu/math.PR/0506189

---------------------------------------------------------------

3444. RANDOM CONFORMAL DYNAMICAL SYSTEMS

Bertrand Deroin & Victor Kleptsyn

We consider random dynamical systems such as groups of conformal
transformations with a probability measure, or transversaly conformal
foliations with a Laplace operator along the leaves, in which case we  
consider
the holonomy pseudo-group. We prove that either there exists a measure
invariant under all the elements of the group (or the pseudo-group),  
or almost
surely a long composition of maps contracts exponentially a ball. We  
deduce
some results about the unique ergodicity.


http://front.math.ucdavis.edu/math.DS/0506204

---------------------------------------------------------------

3445. CONTINUITY THEOREMS FOR THE $M/M/1/N$ QUEUEING SYSTEM

Vyacheslav M. Abramov

In this paper continuity theorems are established for the number of  
losses
during a busy period of the $M/M/1/n$ queue, when the service time  
probability
distribution, slightly different in certain sense from the exponential
distribution, is approximated by that exponential distribution.  
Continuity
theorems are obtained in the form of one or two-side stochastic  
inequalities.
The paper shows how the bounds of these inequalities are changed if  
one or
other assumption, associated with specific properties of the service  
time
distribution (precisely described in the paper), is done.  
Specifically, some
parametric families of service time distributions are discussed, and  
the paper
establishes uniform estimations (given for all possible values of the
parameter) and local estimations (where the parameter is fixed and  
takes only
the given value). The analysis of the paper is based on the level  
crossing
approach and some characterization properties of exponential  
distribution.


http://front.math.ucdavis.edu/math.PR/0506227

---------------------------------------------------------------

3446. SINGULARITY POINTS FOR FIRST PASSAGE PERCOLATION

J. E. Yukich and Yu Zhang

Let a and b be fixed positive scalars. Assign independently to each  
edge in
the two-dimensional integer lattice the value a with probability p or  
the value
b with probability 1-p. For all u and v in the two-dimensional  
integer lattice,
let T(u,v) denote the first passage time between u and v. We show  
that there
are points x in the plane such that the `time constant' in the  
direction of x,
namely lim_{n \to \infty} n^{-1} E_p[T(0, nx)], is not a three times
differentiable function of p.


http://front.math.ucdavis.edu/math.PR/0506241

---------------------------------------------------------------

3447. HARRIS FAMILY OF DISCRETE DISTRIBUTIONS

E. Sandhya and  S. Sherly and  and N. Raju

In this paper we discuss the basic properties of a discrete distribution
introduced by Harris in 1948 and obtain a characterization of it. The
divisibility properties of the distribution are also studied. We  
derive the
moment and maximum likelihood estimators for both the parameters and  
verify
them by simulated observations.


http://front.math.ucdavis.edu/math.ST/0506220

---------------------------------------------------------------

3448. RECONSTRUCTION AND SUBGAUSSIAN OPERATORS

Shahar Mendelson and  Alain Pajor and Nicole Tomczak-Jaegermann

We present a randomized method to approximate any vector $v$ from  
some set $T
\subset \R^n$. The data one is given is the set $T$, and $k$ scalar  
products
$(\inr{X_i,v})_{i=1}^k$, where $(X_i)_{i=1}^k$ are i.i.d. isotropic  
subgaussian
random vectors in $\R^n$, and $k \ll n$. We show that with high  
probability,
any $y \in T$ for which $(\inr{X_i,y})_{i=1}^k$ is close to the data  
vector
$(\inr{X_i,v})_{i=1}^k$ will be a good approximation of $v$, and that  
the
degree of approximation is determined by a natural geometric parameter
associated with the set $T$.
   We also investigate a random method to identify exactly any vector  
which has
a relatively short support using linear subgaussian measurements as  
above. It
turns out that our analysis, when applied to $\{-1,1\}$-valued  
vectors with
i.i.d, symmetric entries, yields new information on the geometry of  
faces of
random $\{-1,1\}$-polytope; we show that a $k$-dimensional random
$\{-1,1\}$-polytope with $n$ vertices is $m$-neighborly for very  
large $m\le
{ck/\log (c' n/k)}$. The proofs are based on new estimates on the  
behavior of
the empirical process $\sup_{f \in F} |k^{-1}\sum_{i=1}^k f^2(X_i) - 
\E f^2 |$
when $F$ is a subset of the $L_2$ sphere. The estimates are given in  
terms of
the $\gamma_2$ functional with respect to the $\psi_2$ metric on $F$,  
and hold
both in exponential probability and in expectation.


http://front.math.ucdavis.edu/math.FA/0506239

---------------------------------------------------------------

3449. LARGE-DEVIATIONS/THERMODYNAMIC APPROACH TO PERCOLATION ON THE  
COMPLETE  GRAPH

Marek Biskup and  Lincoln Chayes and S. Alex Smith

We present a large-deviations/thermodynamic approach to the classic  
problem
of percolation on the complete graph. Specifically, we determine the
large-deviation rate function for the probability that the giant  
component
occupies a fixed fraction of the graph. One consequence is an immediate
derivation of the "cavity" formula for the fraction of sites in the  
giant
component. As a by-product of our analysis we compute also the large- 
deviation
rate functions for the probabilities of the event that the random  
graph is
connected, the event that it contains no loops and the event that it  
contains
only "small" components.


http://front.math.ucdavis.edu/math.PR/0506255

---------------------------------------------------------------

3450. STOCHASTIC INEQUALITIES FOR SINGLE-SERVER LOSS QUEUEING SYSTEMS

Vyacheslav M. Abramov

The present paper provides some new stochastic inequalities for the
characteristics of the $M/GI/1/n$ and $GI/M/1/n$ loss queueing  
systems. These
stochastic inequalities are based on the deepen up- and down- 
crossings method,
and they are stronger than the known stochastic inequalities obtained  
earlier.


http://front.math.ucdavis.edu/math.PR/0505068

---------------------------------------------------------------

3451. BOUNDS ON NON-SYMMETRIC DIVERGENCE MEASURES IN TERMS OF  
SYMMETRIC  DIVERGENCE MEASURES

Inder Jeet Taneja

There are many information and divergence measures exist in the  
literature on
information theory and statistics. The most famous among them are
Kullback-Leibler (1951) relative information and Jeffreys (1951) J- 
divergence.
Sibson (1969) Jensen-Shannon divergence has also found its  
applications in the
literature. The author (1995) studied a new divergence measures based on
arithmetic and geometric means. The measures like harmonic mean  
divergence and
triangular discrimination are also known in the literature. Recently,  
Dragomir
et al. (2001) also studies a new measure similar to J-divergence, we  
call here
the relative J-divergence. Another measures arising due to Jensen- 
Shannon
divergence is also studied by Lin (1991). Here we call it relative
Jensen-Shannon divergence. Relative arithmetic-geometric divergence  
(ref.
Taneja, 2004) is also studied here. All these measures can be written as
particular cases of Csiszar's f-divergence. By putting some  
conditions on the
probability distribution, the aim here is to obtain bounds among the  
measures.


http://front.math.ucdavis.edu/math.PR/0506256

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3452. HARMONIC COORDINATES ON FINITELY CONNECTED FRACTAFOLDS

Alexander Teplyaev

We define finitely connected fractafolds, which are generalizations  
of p.c.f.
self-similar sets introduced by Kigami and of fractafolds introduced by
Strichartz. Any self-similarity is not assumed, and countably infinite
ramification is allowed. We prove that if a fractafold has a  
resistance form in
the sense of Kigami that satisfies certain assumptions, then there  
exists a
weak Riemannian metric, defined almost everywhere, such that the  
energy can be
expressed as the integral of the norm of a weak gradient with respect  
to an
energy measure. This generalizes earlier results by Kusuoka and the  
author.
Furthermore, we prove that if the fractafold can be homeomorphically
represented in harmonic coordinates, then the weak gradient can be  
replaced by
the usual gradient for smooth functions, which generalizes an earlier  
result by
Kigami. We also prove a simple formula for the energy measure  
Laplacian in
harmonic coordinates.


http://front.math.ucdavis.edu/math.PR/0506261

---------------------------------------------------------------

3453. PERCOLATION, BOUNDARY, NOISE: AN EXPERIMENT

Boris Tsirelson

The scaling limit of the critical percolation, is it a black noise? The
answer depends on stability to perturbations concentrated along a  
line. This
text, containing no proofs, reports experimental results that suggest  
the
affirmative answer.


http://front.math.ucdavis.edu/math.PR/0506269

---------------------------------------------------------------

3454. STATISTICS OF EXTREME SPACINGS IN DETERMINANTAL RANDOM POINT  
PROCESSES

Alexander Soshnikov

We study translation-invariant determinantal random point fields on  
the real
line. We prove, under quite general conditions, that the smallest  
nearest
spacings between the particles in a large interval have Poisson  
statistics as
the length of the interval goes to infinity.


http://front.math.ucdavis.edu/math.PR/0506286

---------------------------------------------------------------

3455. RENORMALIZATION ANALYSIS OF CATALYTIC WRIGHT-FISHER DIFFUSIONS

K. Fleischmann and J. M. Swart

Recently, several authors have studied maps where a function,  
describing the
local diffusion matrix of a diffusion process with a linear drift  
towards an
attraction point, is mapped into the average of that function with  
respect to
the unique invariant measure of the diffusion process, as a function  
of the
attraction point. Such mappings arise in the analysis of infinite  
systems of
diffusions indexed by the hierarchical group, with a linear attractive
interaction between the components. In this context, the mappings are  
called
renormalization transformations. We consider such maps for catalytic
Wright-Fisher diffusions. These are diffusions on the unit square  
where the
first component (the catalyst) performs an autonomous Wright-Fisher  
diffusion,
while the second component (the reactant) performs a Wright-Fisher  
diffusion
with a rate depending on the first component through a catalyzing  
function. We
determine the limit of rescaled iterates of renormalization  
transformations
acting on the diffusion matrices of such catalytic Wright-Fisher  
diffusions.


http://front.math.ucdavis.edu/math.PR/0506311

---------------------------------------------------------------

3456. P\'{E}NALISATIONS OF WALSH'S BROWNIAN MOTION

Joseph Najnudel (PMA)

In this paper, we construct a family of probability measures, by
penalizations of a Walsh's Brownian motion with a weight dependent on  
its value
and its local time at a time t. We prove that this family converges to a
probability measure as t tends to infinity, and we study the  
behaviour of this
limit measure.


http://front.math.ucdavis.edu/math.PR/0506329

---------------------------------------------------------------

3457. ON THE SCALING LIMIT OF SIMPLE RANDOM WALK EXCURSION MEASURE IN  
THE  PLANE

Michael J. Kozdron (University of Regina)

We prove that the scaling limit of two-dimensional simple random walk
excursion measure in any bounded, simply connected Jordan domain with  
given
inradius is the Brownian excursion measure, a conformally invariant  
infinite
measure on paths.


http://front.math.ucdavis.edu/math.PR/0506337

---------------------------------------------------------------

3458. LIMITING SEARCH COST DISTRIBUTION FOR THE MOVE-TO-FRONT RULE  
WITH RANDOM  REQUEST PROBABILITIES

Javiera Barrera (MAP5) and  Thierry Huillet (LPTM) and  Christian  
Paroissin  (LMA - PAU)

Consider a list of $n$ files whose popularities are random. These  
files are
updated according to the move-to-front rule and we consider the  
induced Markov
chain at equilibrium. We give the exact limiting distribution of the
search-cost per item as $n$ tends to infinity. Some examples are  
supplied.


http://front.math.ucdavis.edu/math.PR/0506343

---------------------------------------------------------------

3459. FORBIDDEN GAP ARGUMENT FOR PHASE TRANSITIONS PROVED BY MEANS  
OF  CHESSBOARD ESTIMATES

Marek Biskup and Roman Kotecky

Existence of first-order phase transitions is often proved with the  
aid of
reflection positivity and chessboard estimates. The standard approach  
relies on
estimates of correlations in torus measures which yield the existence  
of a
transition point where the free energy has a discontinuous derivative  
with
respect to a suitably chosen variable. In addition, at the transition  
point,
two distinct translation-invariant Gibbs states are extracted from torus
measures in which the one-sided derivatives of the free energy are  
realized as
expectations of a local observable $X$. Here we show that (most of)  
the gap
between these extreme expected values is forbidden: There are no  
shift-ergodic
Gibbs states for which the expectation of $X$ lies deep inside the  
gap. We
point out several recent results based on chessboard estimates where  
our main
theorems provide important additional information concerning the  
structure of
the set of possible thermodynamic equilibria.


http://front.math.ucdavis.edu/math-ph/0505011

---------------------------------------------------------------

3460. A CLASS OF REMARKABLE SUBMARTINGALES (III): MULTIPLICATIVE   
DECOMPOSITIONS AND FREQUENCY OF VANISHING OF NONNEGATIVE SUBMARTINGALES

Ashkan Nikeghbali

In this paper, we establish a multiplicative decomposition formula for
nonnegative local martingales and use it to characterize the set of  
continuous
local submartingales $Y$ of the form $Y=N+A$, where the measure $dA$  
is carried
by the set of zeros of $Y$. In particular, we shall see that in the  
set of all
local submartingales with the same martingale part in the multiplicative
decomposition, these submartingales are the smallest ones. We also  
study some
integrability questions in the multiplicative decomposition and  
interpret the
notion of saturated sets in the light of our results.


http://front.math.ucdavis.edu/math.PR/0506369

---------------------------------------------------------------

3461. ORIENTED PERCOLATION IN ONE-DIMENSIONAL BETA |X-Y|^2, BETA > 1   
RANDOM-CLUSTER MODEL

D. H. U. Marchetti and  V. Sidoravicius and M. E. Vares

We consider the one-dimensional long-range Fortuin--Kasteleyn random- 
cluster
model, generated by the edge occupation probabilities p_{<x,y>} = p  
if |x-y| =
1, 1 - exp{-beta |x-y|^2} otherwise, and weighting factor kappa \geq  
1. We
prove the occurrence of oriented percolation when beta>1 and kappa  
\geq 1,
provided p is chosen sufficiently close to 1. We also show that the  
oriented
truncated connectivity tau ^{prime}(x,y) satisfies tau ^{prime}(x,y)  
\leq C
|x-y|^{-theta} with theta = min(2(beta eta -1),2) where eta = eta(p)  
\nearrow 1
as p \nearrow 1.


http://front.math.ucdavis.edu/math.PR/0506404

---------------------------------------------------------------

3462. FAST COMPUTATION OF THE EXPECTED LOSS OF A LOAN PORTFOLIO  
TRANCHE IN THE  GAUSSIAN FACTOR MODEL: USING HERMITE EXPANSIONS FOR  
HIGHER ACCURACY

P.Okunev

We propose a fast algorithm for computing the expected tranche loss  
in the
Gaussian factor model. We test it on portfolios ranging in size from  
25 (the
size of DJ iTraxx Australia) to 100 (the size of DJCDX.NA.HY) with a  
single
factor Gaussian model and show that the algorithm gives accurate  
results. The
algorithm proposed here is an extension of the algorithm proposed in  
\cite{PO}.
The advantage of the new algorithm is that it works well for  
portfolios of
smaller size for which the normal approximation proposed in \cite{PO}  
in not
sufficiently accurate. The algorithm is intended as an alternative to  
the much
slower Fourier transform based methods \cite{MD}.


http://front.math.ucdavis.edu/math.ST/0506378

---------------------------------------------------------------

3463. A STOCHASTIC PERTURBATION OF INVISCID FLOWS

Gautam Iyer

We consider a stochastic flow with drift $u$ and diffusion coefficient
$\sqrt{2 \nu}$. We demand that the drift be recovered from the flow  
map using
the Weber formula, as in the Eulerian-Lagrangian formulation of the  
Euler
equations. In the absence of diffusion, this will yield the Euler  
equations. We
first prove the existence of such stochastic flows, and that the  
expected value
of this process approximates the Navier-Stokes equations (with  
viscosity $\nu$)
to order $O(t^{3/2})$. As a result of our estimates we also obtain a  
local
existence and uniqueness results for the Navier-Stokes equations.


http://front.math.ucdavis.edu/math.AP/0505066

---------------------------------------------------------------

3464. MODERATE DEVIATIONS AND LAWS OF THE ITERATED LOGARITHM FOR THE   
RENORMALIZED SELF-INTERSECTION LOCAL TIMES OF PLANAR RANDOM WALKS

Richard F. Bass and  Xia Chen and  and Jay Rosen

Let B_n be the number of self-intersections of a symmetric random  
walk with
finite second moments in the integer planar lattice. We obtain moderate
deviation estimates for B_n - E B_n and E B_n- B_n, which are given  
in terms of
the best constant of a certain Gagliardo-Nirenberg inequality. We  
also prove
the corresponding laws of the iterated logarithm.


http://front.math.ucdavis.edu/math.PR/0506414

---------------------------------------------------------------

3465. SMOOTHENING EFFECT OF QUENCHED DISORDER ON POLYMER DEPINNING  
TRANSITIONS

G. Giacomin (1) and  F. L. Toninelli (2) ((1) Universite' de Paris 7  
and  (2)  ENS Lyon, UMR--CNRS 5672)

We consider general disordered models of pinning of directed polymers  
on a
defect line. This class contains in particular the disordered
$(1+1)$--dimensional interface wetting model, a version of the  
Poland--Scheraga
model of DNA denaturation and other $(1+d)$--dimensional polymers in
interaction with flat interfaces. We consider also the case of  
copolymers with
adsorption at a selective interface.
   Under quite general conditions, these models are known to have a
(de)localization transition at some critical line in the phase  
diagram. In this
work we prove in particular that, as soon as disorder is present, the
transition is at least of second order, in the sense that the free  
energy is
differentiable at the critical line, so that the order parameter  
vanishes
continuously at the transition. On the other hand, it is known that the
corresponding non--disordered models can have a first order (de) 
localization
transition, with a discontinuous first derivative. Our result shows  
therefore
that the presence of the disorder has really a smoothening effect on the
transition.


http://front.math.ucdavis.edu/math.PR/0506431

---------------------------------------------------------------

3466. ON A PROBLEM OF K. MAHLER: DIOPHANTINE APPROXIMATION AND CANTOR  
SETS

Jason Levesley and  Cem Salp and Sanju Velani

Let $K$ denote the middle third Cantor set and ${\cal A}:= \{3^n : n  
= 0,1,2,
 >... \} $. Given a real, positive function $\psi$ let $ W_{\cal A} 
(\psi)$
denote the set of real numbers $x$ in the unit interval for which  
there exist
infinitely many $(p,q) \in \Z \times {\cal A} $ such that $ |x - p/q|  
< \psi(q)
$. The analogue of the Hausdorff measure version of the Duffin-Schaeffer
conjecture is established for $ W_{\cal A}(\psi) \cap K $. One of the
consequences of this is that there exist very well approximable  
numbers, other
than Liouville numbers, in $K$ -- an assertion attributed to K. Mahler.


http://front.math.ucdavis.edu/math.NT/0505074

---------------------------------------------------------------

3467. GAUSSIAN ESTIMATES FOR SYMMETRIC SIMPLE EXCLUSION PROCESSES

C. Landim

We prove Gaussian tail estimates for the transition probability of $n$
particles evolving as symmetric exclusion processes on $\bb Z^d$,  
improving
results obtained in \cite{l}. We derive from this result a non- 
equilibrium
Boltzmann-Gibbs principle for the symmetric simple exclusion process in
dimension 1 starting from a product measure with slowly varying  
parameter.


http://front.math.ucdavis.edu/math.PR/0505089

---------------------------------------------------------------

3468. THE PHASE TRANSITION IN INHOMOGENEOUS RANDOM GRAPHS

Bela Bollobas and  Svante Janson and  Oliver Riordan

We introduce a very general model of an inhomogenous random graph with
independence between the edges, which scales so that the number of  
edges is
linear in the number of vertices. This scaling corresponds to the p=c/ 
n scaling
for G(n,p) used to study the phase transition; also, it seems to be a  
property
of many large real-world graphs. Our model includes as special cases  
many
models previously studied.
   We show that under one very weak assumption (that the expected  
number of
edges is `what it should be'), many properties of the model can be  
determined,
in particular the critical point of the phase transition, and the  
size of the
giant component above the transition. We do this by relating our  
random graphs
to branching processes, which are much easier to analyze.
   We also consider other properties of the model, showing, for  
example, that
when there is a giant component, it is `stable': for a typical random  
graph, no
matter how we add or delete o(n) edges, the size of the giant  
component does
not change by more than o(n). We believe that this result is new even  
for the
classical graph G(n,c/n), in which case the proof is much simpler.


http://front.math.ucdavis.edu/math.PR/0504589

---------------------------------------------------------------

3469. SUPERDIFFUSIVITY OF TWO DIMENSIONAL LATTICE GAS MODELS

C. Landim and  J. A. Ramirez and  H.-T. Yau

It was proved \cite{EMYa, QY} that stochastic lattice gas dynamics  
converge
to the Navier-Stokes equations in dimension $d=3$ in the  
incompressible limits.
In particular, the viscosity is finite. We proved that, on the other  
hand, the
viscosity for a two dimensional lattice gas model diverges faster  
than $\log
\log t$. Our argument indicates that the correct divergence rate is $ 
(\log
t)^{1/2}$. This problem is closely related to the logarithmic  
correction of the
time decay rate for the velocity auto-correlation function of a tagged
particle.


http://front.math.ucdavis.edu/math.PR/0505090

---------------------------------------------------------------

3470. NONEQUILIBRIUM CENTRAL LIMIT THEOREM FOR A TAGGED PARTICLE IN  
SYMMETRIC  SIMPLE EXCLUSION

M. D. Jara and  C. Landim

We prove a nonequilibirum central limit theorem for the position of a  
tagged
particle in the one-dimensional nearest-neighbor symmetric simple  
exclusion
process under diffusive scaling starting from a Bernoulli product  
measure
associated to a smooth profile $\rho_0:\bb R\to [0,1]$.


http://front.math.ucdavis.edu/math.PR/0505091

---------------------------------------------------------------

3471. A MICROSCOPIC MODEL FOR STEFAN'S MELTING AND FREEZING PROBLEM

Claudio Landim and Glauco Valle

We study a class of one-dimensional interacting particle systems with  
random
boundaries as a microscopic model for Stefan's melting and freezing  
problem. We
prove that under diffusive rescaling these particle systems exhibit a
hydrodynamic behavior described by the solution of a Cauchy-Stefan  
problem.


http://front.math.ucdavis.edu/math.PR/0505092

---------------------------------------------------------------

3472. A DETERMINANTAL FORMULA FOR THE GOE TRACY-WIDOM DISTRIBUTION

Patrik L. Ferrari (1) and Herbert Spohn (1) ((1) TU-Muenchen)

Investigating the long time asymptotics of the totally asymmetric simple
exclusion process, Sasamoto obtains rather indirectly a formula for  
the GOE
Tracy-Widom distribution. We establish that his novel formula indeed  
agrees
with more standard expressions.


http://front.math.ucdavis.edu/math-ph/0505012

---------------------------------------------------------------

3473. ASYMPTOTIC ANALYSIS OF LOSSES IN THE $GI/M/M/N$ QUEUEING SYSTEM  
AS $N$  INCREASES TO INFINITY

Vyacheslav M. Abramov

The paper studies asymptotic behavior of the loss probability for the
$GI/M/m/n$ queueing system as $n$ increases to infinity. The approach  
of the
paper is based on applications of classic results of Tak\'acs (1967)  
and the
Tauberian theorem with remainder of Postnikov (1979-1980) associated  
with the
recurrence relation of convolution type. The main result of the paper is
associated with asymptotic behavior of the loss probability.  
Specifically it is
shown that in some cases (precisely described in the paper) where the  
load of
the system approaches 1 from the left and $n$ increases to infinity,  
the loss
probability of the $GI/M/m/n$ queue becomes asymptotically  
independent of the
parameter $m$.


http://front.math.ucdavis.edu/math.PR/0505127

---------------------------------------------------------------

3474. COMPUTABLE INFINITE DIMENSIONAL FILTERS WITH APPLICATIONS TO  
DISCRETIZED  DIFFUSION PROCESSES

Mireille Chaleyat-Maurel (PMA and  MAP5) and  Valentine Genon-Catalot  
(MAP5)

Let us consider a pair signal-observation ((xn,yn),n 0) where the  
unobserved
signal (xn) is a Markov chain and the observed component is such  
that, given
the whole sequence (xn), the random variables (yn) are independent  
and the
conditional distribution of yn only depends on the corresponding  
state variable
xn. The main problems raised by these observations are the prediction  
and
filtering of (xn). We introduce sufficient conditions allowing to obtain
computable filters using mixtures of distributions. The filter system  
may be
finite or infinite dimensional. The method is applied to the case  
where the
signal xn = Xn is a discrete sampling of a one dimensional diffusion  
process:
Concrete models are proved to fit in our conditions. Moreover, for these
models, exact likelihood inference based on the observation  
(y0,...,yn) is
feasable.


http://front.math.ucdavis.edu/math.PR/0505153

---------------------------------------------------------------

3475. SCHOENBERG'S THEOREM VIA THE LAW OF LARGE NUMBERS

Davar Khoshnevisan

A classical theorem of S. Bochner states that a function
   $f:R^n \to C$ is the Fourier transform of a finite Borel measure  
if and only
if $f$ is positive definite. In 1938, I. Schoenberg found a beautiful  
converse
to Bochner's theorem.
   We present a non-technical derivation of of Schoenberg's theorem  
that relies
chiefly on the law of large numbers of classical probability theory.


http://front.math.ucdavis.edu/math.PR/0504603

---------------------------------------------------------------

3476. RANDOM SYMMETRIC MATRICES ARE ALMOST SURELY NON-SINGULAR

Kevin Costello and  Terence Tao and  Van Vu

Let $Q_n$ denote a random symmetric $n$ by $n$ matrix, whose upper  
diagonal
entries are i.i.d. Bernoulli random variables (which take values 0  
and 1 with
probability 1/2). We prove that $Q_n$ is non-singular with probability
$1-O(n^{-1/8+\delta})$ for any fixed $\delta > 0$. The proof uses a  
quadratic
version of Littlewood-Offord type results concerning the concentration
functions of random variables and can be extended for more general  
models of
random matrices.


http://front.math.ucdavis.edu/math.PR/0505156

---------------------------------------------------------------

3477. REGENERATIVE COMPOSITIONS IN THE CASE OF SLOW VARIATION

Andrew D. Barbour and Alexander V. Gnedin

For $S$ a subordinator and $\Pi_n$ an independent Poisson process of
intensity $ne^{-x}, x>0,$ we are interested in the number $K_n$ of  
gaps in the
range of $S$ that are hit by at least one point of $\Pi_n$. Extending  
previous
studies in \cite{Bernoulli, GPYI, GPYII} we focus on the case when  
the tail of
the L{\'e}vy measure of $S$ is slowly varying. We view $K_n$ as the  
terminal
value of a random process ${\cal K}_n$, and provide an asymptotic  
analysis of
the fluctuations of ${\cal K}_n$, as $n\to\infty$, for a wide  
spectrum of
situations.


http://front.math.ucdavis.edu/math.PR/0505171

---------------------------------------------------------------

3478. LOGARITHMIC SOBOLEV INEQUALITIES AND CONCENTRATION OF MEASURE  
FOR CONVEX  FUNCTIONS AND POLYNOMIAL CHAOSES

Radoslaw Adamczak

We prove logarithmic Sobolev inequalities and concentration results for
convex functions and a class of product random vectors. The results  
are used to
derive tail and moment inequalities for chaos variables (in spirit of  
Talagrand
and Arcones, Gine). We also show that the same proof may be used for  
chaoses
generated by log-concave random variables, recovering results by  
Lochowski and
present an application to exponential integrability of Rademacher chaos.


http://front.math.ucdavis.edu/math.PR/0505175

---------------------------------------------------------------

3479. GENERALIZED ITO FORMULAE AND SPACE-TIME LEBESGUE-STIELTJES  
INTEGRALS OF  LOCAL TIMES

K.D. Elworthy and  A. Truman and  H.Z. Zhao

Generalised Ito formulae are proved for time dependent functions of
continuous real valued semi-martingales.The conditions involve left  
space and
time first derivatives, with the left space derivative required to  
have locally
bounded 2-dimensional variation. In particular a class of functions with
discontinuous first derivative is included. An estimate of Krylov allows
further weakening of these conditions when the semi-martingale is a  
diffusion.


http://front.math.ucdavis.edu/math.PR/0505195

---------------------------------------------------------------

3480. A GENERALIZED IT$\HAT {\RM O}$'S FORMULA IN TWO-DIMENSIONS AND   
STOCHASTIC LEBESGUE-STIELTJES INTEGRALS

Chunrong Feng and  Huaizhong Zhao

A generalized It${\hat {\rm o}}$ formula for time dependent functions of
two-dimensional continuous semi-martingales is proved. The formula  
uses the
local time of each coordinate process of the semi-martingale, left  
space and
time first derivatives and second derivative $\nabla_1^- \nabla_2^-f$  
only
which are assumed to be of locally bounded variation in certain  
variables, and
stochastic Lebesgue-Stieltjes integrals of two parameters.The two- 
parameter
integral is defined as a natural generalization of the It${\hat {\rm  
o}}$
integral and Lebesgue-Stieltjes integral through a type of It${\hat  
{\rm o}}$
isometry formula.


http://front.math.ucdavis.edu/math.PR/0505196

---------------------------------------------------------------

3481. RELATIVE DIVERGENCE MEASURES AND INFORMATION INEQUALITIES

Inder Jeet Taneja

There are many information and divergence measures exist in the  
literature on
information theory and statistics. The most famous among them are
Kullback-Leiber's (1951)relative information and Jeffreys (1946) J- 
divergence,
Information radius or Jensen difference divergence measure due to  
Sibson (1969)
also known in the literature. Burbea and Rao (1982) has also found its
applications in the literature. Taneja (1995) studied another kind of
divergence measure based on arithmetic and geometric means. These three
divergence measures bear a good relationship among each other. But  
there are
another measures arising due to J-divergence, JS-divergence and AG- 
divergence.
These measures we call here relative divergence measures or non- 
symmetric
divergence measures. Here our aim is to obtain bounds on symmetric and
non-symmetric divergence measures in terms of relative information of  
type s
using properties of Csiszar's f-divergence.


http://front.math.ucdavis.edu/math.PR/0505204

---------------------------------------------------------------

3482. PAINLEVE FORMULAS OF THE LIMITING DISTRIBUTIONS FOR NON-NULL  
COMPLEX  SAMPLE COVARIANCE MATRICES

Jinho Baik

In a recent study of large non-null sample covariance matrices, a new
sequence of functions generalizing the GUE Tracy-Widom distribution  
of random
matrix theory was obtained. This paper derives Painlev\'e formulas of  
these
functions and use them to prove that they are indeed distribution  
functions.
Applications of these new distribution functions to last passage  
percolation,
queues in tandem and totally asymmetric simple exclusion process are  
also
discussed. As a part of the proof, a representation of orthogonal  
polynomials
on the unit circle in terms of an operator on a discrete set is  
presented.


http://front.math.ucdavis.edu/math.PR/0504606

---------------------------------------------------------------

3483. CLASSICAL SOLUTIONS TO REACTION-DIFFUSION SYSTEMS FOR HEDGING  
PROBLEMS  WITH INTERACTING ITO AND POINT PROCESSES

Dirk Becherer and Martin Schweizer

We use probabilistic methods to study classical solutions for systems of
interacting semilinear parabolic partial differential equations. In a  
modeling
framework for a financial market with interacting Ito and point  
processes, such
PDEs are shown to provide a natural description for the solution of  
hedging and
valuation problems for contingent claims with a recursive payoff  
structure.


http://front.math.ucdavis.edu/math.PR/0505208

---------------------------------------------------------------

3484. DRIFT RATE CONTROL OF A BROWNIAN PROCESSING SYSTEM

Bar Ata and  J. M. Harrison and L. A. Shepp

A system manager dynamically controls a diffusion process Z that  
lives in a
finite interval [0,b]. Control takes the form of a negative drift  
rate \theta
that is chosen from a fixed set A of available values. The controlled  
process
evolves according to the differential relationship dZ=dX-\theta(Z) dt 
+dL-dU,
where X is a (0,\sigma) Brownian motion, and L and U are increasing  
processes
that enforce a lower reflecting barrier at Z=0 and an upper  
reflecting barrier
at Z=b, respectively. The cumulative cost process increases according  
to the
differential relationship d\xi =c(\theta(Z)) dt+p dU, where c(\cdot)  
is a
nondecreasing cost of control and p>0 is a penalty rate associated with
displacement at the upper boundary. The objective is to minimize long- 
run
average cost. This problem is solved explicitly, which allows one to  
also solve
the following, essentially equivalent formulation: minimize the long-run
average cost of control subject to an upper bound constraint on the  
average
rate at which U increases. The two special problem features that  
allow an
explicit solution are the use of a long-run average cost criterion,  
as opposed
to a discounted cost criterion, and the lack of state-related costs  
other than
boundary displacement penalties. The application of this theory to power
control in wireless communication is discussed.


http://front.math.ucdavis.edu/math.PR/0505210

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3485. SAMPLE-PATH LARGE DEVIATIONS FOR TANDEM AND PRIORITY QUEUES  
WITH  GAUSSIAN INPUTS

Michel Mandjes and Miranda van Uitert

This paper considers Gaussian flows multiplexed in a queueing network. A
single node being a useful but often incomplete setting, we examine more
advanced models. We focus on a (two-node) tandem queue, fed by a  
large number
of Gaussian inputs. With service rates and buffer sizes at both nodes  
scaled
appropriately, Schilder's sample-path large-deviations theorem can be  
applied
to calculate the asymptotics of the overflow probability of the  
second queue.
More specifically, we derive a lower bound on the exponential decay  
rate of
this overflow probability and present an explicit condition for the  
lower bound
to match the exact decay rate. Examples show that this condition  
holds for a
broad range of frequently used Gaussian inputs. The last part of the  
paper
concentrates on a model for a single node, equipped with a priority  
scheduling
policy. We show that the analysis of the tandem queue directly  
carries over to
this priority queueing system.


http://front.math.ucdavis.edu/math.PR/0505214

---------------------------------------------------------------

3486. THE MOTION OF A SECOND CLASS PARTICLE FOR THE TASEP STARTING  
FROM A  DECREASING SHOCK PROFILE

Thomas Mountford and Herve Guiol

We prove a strong law of large numbers for the location of the second  
class
particle in a totally asymmetric exclusion process when the process  
is started
initially from a decreasing shock. This completes a study initiated  
in Ferrari
and Kipnis [Ann. Inst. H. Poincare Probab. Statist. 13 (1995) 143-154].


http://front.math.ucdavis.edu/math.PR/0505216

---------------------------------------------------------------

3487. METRIC BASED UP-SCALING

Houman Owhadi and Lei Zhang

Heterogeneous multi-scale structures can be found everywhere in  
nature. Can
these structures be accurately simulated at a coarse level?  
Homogenization
theory allows us to do so under the assumptions of ergodicity and scale
separation by transferring bulk (averaged) information from sub-grid  
scales to
computational scales. Can we get rid of these assumptions? can we  
compress a
PDE with arbitrary coefficients? Surprisingly the answer is yes, is  
rigorous
and based on a new form of compensation. We will consider divergence  
form
elliptic operators in dimension $n\geq 2$ to introduce this method.  
Although
solutions of these operators are only H\"{o}lder continuous, we show  
that their
regularity with respect to Harmonic mappings is $C^{1,\alpha}$. It  
follows that
these PDEs can be up-scaled by transferring a new metric in addition to
traditional bulk quantities from small scales into coarse scales and  
error
bounds can be given.


http://front.math.ucdavis.edu/math.NA/0505223

---------------------------------------------------------------

3488. BOOTSTRAP CENTRAL LIMIT THEOREM FOR CHAINS OF INFINITE ORDER  
VIA MARKOV  APPROXIMATIONS

P. Collet and  D. Duarte and A. Galves

We present a new approach to the bootstrap for chains of infinite order
taking values on a finite alphabet. It is based on a sequential  
Bootstrap
Central Limit Theorem for the sequence of canonical Markov  
approximations of
the chain of infinite order. Combined with previous results on the  
rate of
approximation this leads to a Central Limit Theorem for the bootstrapped
estimator of the sample mean which is the main result of this paper.


http://front.math.ucdavis.edu/math.PR/0505232

---------------------------------------------------------------

3489. BOUNDS ON TRIANGULAR DISCRIMINATION, HARMONIC MEAN AND  
SYMMETRIC  CHI-SQUARE DIVERGENCES

Inder Jeet Taneja

There are many information and divergence measures exist in the  
literature on
information theory and statistics. The most famous among them are
Kullback-Leiber relative information and Jeffreys J-divergence. The  
measures
like, Bhattacharya distance, Hellinger discrimination, Chi-square  
divergence,
triangular discrimination and harmonic mean divergence are also  
famous in the
literature on statistics. In this paper we have obtained bounds on  
triangular
discrimination and symmetric chi-square divergence in terms of relative
information of type s using Csiszar's f-divergence. A relationship among
triangular discrimination and harmonic mean divergence is also given.


http://front.math.ucdavis.edu/math.PR/0505238

---------------------------------------------------------------

3490. ASYMPTOTIC BEHAVIOR OF A METAPOPULATION MODEL

A. D. Barbour and A. Pugliese

We study the behavior of an infinite system of ordinary differential
equations modeling the dynamics of a metapopulation, a set of (discrete)
populations subject to local catastrophes and connected via migration  
under a
mean field rule; the local population dynamics follow a generalized  
logistic
law. We find a threshold below which all the solutions tend to total  
extinction
of the metapopulation, which is then the only equilibrium; above the  
threshold,
there exists a unique equilibrium with positive population, which,  
under an
additional assumption, is globally attractive. The proofs employ  
tools from the
theories of Markov processes and of dynamical systems.


http://front.math.ucdavis.edu/math.PR/0505240

---------------------------------------------------------------

3491. ON THE CONVERGENCE FROM DISCRETE TO CONTINUOUS TIME IN AN  
OPTIMAL  STOPPING PROBLEM

Paul Dupuis and Hui Wang

We consider the problem of optimal stopping for a one-dimensional  
diffusion
process. Two classes of admissible stopping times are considered. The  
first
class consists of all nonanticipating stopping times that take values in
[0,\infty], while the second class further restricts the set of  
allowed values
to the discrete grid {nh:n=0,1,2,...,\infty} for some parameter h>0.  
The value
functions for the two problems are denoted by V(x) and V^h(x),  
respectively. We
identify the rate of convergence of V^h(x) to V(x) and the rate of  
convergence
of the stopping regions, and provide simple formulas for the rate  
coefficients.


http://front.math.ucdavis.edu/math.PR/0505241

---------------------------------------------------------------

3492. EXCHANGEABLE, GIBBS AND EQUILIBRIUM MEASURES FOR MARKOV SUBSHIFTS

Jon. Aaronson and  Hitoshi Nakada

We study a class of strongly irreducible, multidimensional, topological
Markov shifts, comparing two notions of "symmetric measure":  
exchangeability
and the Gibbs property. We show that equilibrium measures for such  
shifts
(unique and weak Bernoulli in the one dimensional case) exhibit a  
variety of
spectral properties.


http://front.math.ucdavis.edu/math.PR/0505011

---------------------------------------------------------------

3493. ON UTILITY MAXIMIZATION IN DISCRETE-TIME FINANCIAL MARKET MODELS

Miklos Rasonyi and Lukasz Stettner

We consider a discrete-time financial market model with finite time  
horizon
and give conditions which guarantee the existence of an optimal  
strategy for
the problem of maximizing expected terminal utility. Equivalent  
martingale
measures are constructed using optimal strategies.


http://front.math.ucdavis.edu/math.PR/0505243

---------------------------------------------------------------

3494. ACCELERATING DIFFUSIONS

Chii-Ruey Hwang and  Shu-Yin Hwang-Ma and Shuenn-Jyi Sheu

Let U be a given function defined on R^d and \pi(x) be a density  
function
proportional to \exp -U(x). The following diffusion X(t) is often  
used to
sample from \pi(x), dX(t)=-\nabla U(X(t)) dt+\sqrt2 dW(t),\qquad X(0) 
=x_0. To
accelerate the convergence, a family of diffusions with \pi(x) as  
their common
equilibrium is considered, dX(t)=\bigl(-\nabla U(X(t))+C(X(t))\bigr)  
dt+\sqrt2
dW(t),\qquad X(0)=x_0. Let L_C be the corresponding infinitesimal  
generator.
The spectral gap of L_C in L^2(\pi) (\lambda (C)), and the  
convergence exponent
of X(t) to \pi in variational norm (\rho(C)), are used to describe the
convergence rate, where \lambda(C)= Sup{real part of \mu\dvtx\mu is  
in the
spectrum of L_C, \mu is not zero}, {-2.8cm}\rho(C) = Inf\biggl{\rho 
\dvtx\int |
p(t,x,y) -\pi(y)| dy \le g(x) e^{\rho t}\biggr}.Roughly speaking, L_C  
is a
perturbation of the self-adjoint L_0 by an antisymmetric operator C 
\cdot\nabla,
where C is weighted divergence free. We prove that \lambda (C)\le  
\lambda (0)
and equality holds only in some rare situations. Furthermore, \rho(C)\le
\lambda (C) and equality holds for C=0. In other words, adding an  
extra drift,
C(x), accelerates convergence. Related problems are also discussed.


http://front.math.ucdavis.edu/math.PR/0505245

---------------------------------------------------------------

3495. CRAMER'S ESTIMATE FOR A REFLECTED LEVY PROCESS

R. A. Doney and R. A. Maller

The natural analogue for a Levy process of Cramer's estimate for a  
reflected
random walk is a statement about the exponential rate of decay of the  
tail of
the characteristic measure of the height of an excursion above the  
minimum. We
establish this estimate for any Levy process with finite negative  
mean which
satisfies Cramer's condition, and give an explicit formula for the  
limiting
constant. Just as in the random walk case, this leads to a Poisson limit
theorem for the number of ``high excursions.''


http://front.math.ucdavis.edu/math.PR/0505246

---------------------------------------------------------------

3496. SUMMATION TEST FOR GAP PENALTIES AND STRONG LAW OF THE LOCAL  
ALIGNMENT  SCORE

Hock Peng Chan

A summation test is proposed to determine admissible types of gap  
penalties
for logarithmic growth of the local alignment score. We also define a
converging sequence of log moment generating functions that provide the
constants associated with the large deviation rate and logarithmic  
strong law
of the local alignment score and the asymptotic number of matches in the
optimal local alignment.


http://front.math.ucdavis.edu/math.PR/0505247

---------------------------------------------------------------

3497. THE BRANCHING PROCESS WITH LOGISTIC GROWTH

Amaury Lambert

In order to model random density-dependence in population dynamics, we
construct the random analogue of the well-known logistic process in the
branching process' framework. This density-dependence corresponds to
intraspecific competition pressure, which is ubiquitous in ecology, and
translates mathematically into a quadratic death rate. The logistic  
branching
process, or LB-process, can thus be seen as (the mass of) a  
fragmentation
process (corresponding to the branching mechanism) combined with  
constant
coagulation rate (the death rate is proportional to the number of  
possible
coalescing pairs). In the continuous state-space setting, the LB- 
process is a
time-changed (in Lamperti's fashion) Ornstein-Uhlenbeck type process.  
We obtain
similar results for both constructions: when natural deaths do not  
occur, the
LB-process converges to a specified distribution; otherwise, it goes  
extinct
a.s. In the latter case, we provide the expectation and the Laplace  
transform
of the absorption time, as a functional of the solution of a Riccati
differential equation. We also show that the quadratic regulatory  
term allows
the LB-process to start at infinity, despite the fact that births occur
infinitely often as the initial state goes to \infty. This result can  
be viewed
as an extension of the pure-death process starting from infinity  
associated to
Kingman's coalescent, when some independent fragmentation is added.


http://front.math.ucdavis.edu/math.PR/0505249

---------------------------------------------------------------

3498. THE OSCILLATORY DISTRIBUTION OF DISTANCES IN RANDOM TRIES

Costas A. Christophi and Hosam M. Mahmoud

We investigate \Delta_n, the distance between randomly selected pairs of
nodes among n keys in a random trie, which is a kind of digital tree.
Analytical techniques, such as the Mellin transform and an excursion  
between
poissonization and depoissonization, capture small fluctuations in  
the mean and
variance of these random distances. The mean increases  
logarithmically in the
number of keys, but curiously enough the variance remains O(1), as n 
\to\infty.
It is demonstrated that the centered random variable
\Delta_n^*=\Delta_n-\lfloor2\log_2n\rfloor does not have a limit  
distribution,
but rather oscillates between two distributions.


http://front.math.ucdavis.edu/math.PR/0505259

---------------------------------------------------------------

3499. SUBGEOMETRIC ERGODICITY OF STRONG MARKOV PROCESSES

G. Fort and G. O. Roberts

We derive sufficient conditions for subgeometric f-ergodicity of  
strongly
Markovian processes. We first propose a criterion based on modulated  
moment of
some delayed return-time to a petite set. We then formulate a  
criterion for
polynomial f-ergodicity in terms of a drift condition on the generator.
Applications to specific processes are considered, including Langevin  
tempered
diffusions on R^n and storage models.


http://front.math.ucdavis.edu/math.PR/0505260

---------------------------------------------------------------

3500. ASYMPTOTIC RESULTS ON THE MOMENTS OF THE RATIO OF THE RANDOM  
SUM OF  SQUARES TO THE SQUARE OF THE RANDOM SUM

S.A. Ladoucette

Let \{X_1, X_2, ...\} be a sequence of positive independent and  
identically
distributed random variables of Pareto-type with index \alpha>0 and  
let \{N(t);
t\geq 0\} be a mixed Poisson process independent of the X_i's. For t 
\geq 0,
define T_{N(t)}:=\frac{X_1^2 + X_2^2 + ... + X_{N(t)}^2} {(X_1 + X_2  
+ ... +
X_{N(t)})^2} if N(t)\geq 1 and T_{N(t)}:=0 otherwise.
   We derive the limiting behavior of the k-th moment of T_{N(t)},
k\in\mathbb{N}, by using the theory of functions of regular variation  
and an
integral representation for \mathbb{E}\{T_{N(t)}^k\}. We also point  
out the
connection between T_{N(t)} and the sample coefficient of variation  
which is a
popular risk measure in practical applications.


http://front.math.ucdavis.edu/math.PR/0505265

---------------------------------------------------------------

3501. A CAPTURE PROBLEM IN BROWNIAN MOTION AND EIGENVALUES OF  
SPHERICAL  DOMAINS

Jesse Ratzkin and Andrejs Treibergs

We resolve a question of Bramson and Griffeath by showing that the  
expected
capture time of four independent Brownian predators pursuing one  
Brownian prey
on a line is finite. Our main tool is an eigenvalue estimate for a  
particular
spherical domain, which we obtain by a coning construction and domain
perturbation.


http://front.math.ucdavis.edu/math.PR/0505274

---------------------------------------------------------------

3502. ITERATED BROWNIAN MOTION IN BOUNDED DOMAINS IN R^N

Erkan Nane

Let $\tau_{D}(Z) $ is the first exit time of iterated Brownian motion  
from a
domain $D \subset \RR{R}^{n}$ started at $z\in D$ and let $P_{z}[\tau_ 
{D}(Z)
 >t]$ be its distribution. In this paper we establish the exact  
asymptotics of
$P_{z}[\tau_{D}(Z) >t]$ over bounded domains as an extension of the  
result in
DeBlassie \cite{deblassie}, for $z\in D$ $$ P_{z}[\tau_{D}(Z)>t] 
\approx t^{1/2}
\exp(-{3/2}\pi^{2/3}\lambda_{D}^{2/3}t^{1/3}), as t\to\infty . $$ We  
also study
asymptotics of the life time of Brownian-time Brownian motion (BTBM),
$Z^{1}_{t}=z+X(Y(t))$, where $X_{t}$ and $Y_{t}$ are independent
one-dimensional Brownian motions.


http://front.math.ucdavis.edu/math.PR/0505026

---------------------------------------------------------------

3503. SPECTRAL PROPERTIES OF THE LAPLACIAN ON BOND-PERCOLATION GRAPHS

Werner Kirsch and  Peter M\"uller

Bond-percolation graphs are random subgraphs of the d-dimensional  
integer
lattice generated by a standard bond-percolation process. The  
associated graph
Laplacians, subject to Dirichlet or Neumann conditions at cluster  
boundaries,
represent bounded, self-adjoint, ergodic random operators with off- 
diagonal
disorder. They possess almost surely the non-random spectrum [0,4d]  
and a
self-averaging integrated density of states. The integrated density  
of states
is shown to exhibit Lifshits tails at both spectral edges in the
non-percolating phase. While the characteristic exponent of the  
Lifshits tail
for the Dirichlet (Neumann) Laplacian at the lower (upper) spectral  
edge equals
d/2, and thus depends on the spatial dimension, this is not the case  
at the
upper (lower) spectral edge, where the exponent equals 1/2.


http://front.math.ucdavis.edu/math-ph/0407047

---------------------------------------------------------------

3504. A NOTE ON MULTITYPE BRANCHING PROCESSES WITH IMMIGRATION IN A  
RANDOM  ENVIRONMENT

Alexander Roitershtein

We consider a multitype branching process with immigration in a random
environment introduced by Key in [12]. It was shown by Key that the  
branching
process is subcritical in the sense that it converges to a proper  
limit law. We
complement this result by a strong law of large numbers and a central  
limit
theorem for the partial sums of the process. In addition, we study the
asymptotic behavior of oscillations of the branching process, i.e. of  
the
random segments between successive times when the extinction occurs  
and the
process starts afresh with the next wave of the immigration.


http://front.math.ucdavis.edu/math.PR/0505292

---------------------------------------------------------------

3505. ESTIMATES OF MOMENTS AND TAILS OF GAUSSIAN CHAOSES

Rafal Latala

We derive two sided estimates on moments and tails of homogenous  
Gaussian
chaoses of any order. Estimates are exact up to constants depending  
only on the
order of chaoses.


http://front.math.ucdavis.edu/math.PR/0505313

---------------------------------------------------------------

3506. NON STOPPING TIMES AND STOPPING THEOREMS

Ashkan Nikeghbali

Given a random time, we characterize the set of martingales for which  
the
stopping theorems still hold. We also investigate how the stopping  
theorems are
modified when we consider arbitrary random times. To this end, we  
introduce
some families of martingales with remarkable properties. We also  
investigate,
in the Brownian setting, the relationships between a given random  
time and the
underlying Brownian Motion in the progressively enlarged filtration with
respect to this random time.


http://front.math.ucdavis.edu/math.PR/0505316

---------------------------------------------------------------

3507. LIMITING BEHAVIOR OF A DIFFUSION IN AN ASYMPTOTICALLY STABLE  
ENVIRONMENT

Arvind Singh (PMA)

Let $V$ be a two sided random walk and let $X$ denote a real valued  
diffusion
process with generator ${1/2}e^{V([x])}\frac{d}{dx}(e^{-V([x])}\frac 
{d}{dx})$.
This process is known to be the continuous equivalent of the one  
dimensional
random walk in random environment with potential $V$. Hu and Shi (1997)
described the L\'evy classes of $X$ in the case where $V$ behaves  
approximately
like a Brownian motion. In this paper, based on some fine results on the
fluctuations of random walks and stable processes, we obtain an  
accurate image
of the almost sure limiting behavior of $X$ when $V$ behaves  
asymptotically
like a stable process. These results also apply for the corresponding  
random
walk in random environment.


http://front.math.ucdavis.edu/math.PR/0505332

---------------------------------------------------------------

3508. THE EFFICIENT EVALUATION OF THE HYPERGEOMETRIC FUNCTION OF A  
MATRIX  ARGUMENT

Plamen Koev and  Alan Edelman

We present new algorithms that efficiently approximate the  
hypergeometric
function of a matrix argument through its expansion as a series of Jack
functions. Our algorithms exploit the combinatorial properties of the  
Jack
function, and have complexity that is only linear in the size of the  
matrix.


http://front.math.ucdavis.edu/math.PR/0505344

---------------------------------------------------------------

3509. DETERMINANTAL POINT PROCESSES AND FERMIONIC FOCK SPACE

Neretin Yurii A

We construct a canonical embedding of the space $L^2$ over a  
determinantal
point process to the fermionic Fock space. Equivalently, we show that a
determinantal process is the spectral measure for some explicit  
commutative
group of Gaussian operators in the fermionic Fock space.


http://front.math.ucdavis.edu/math-ph/0505041

---------------------------------------------------------------

3510. ON THE BEST CONSTANTS IN SOME NON-COMMUTATIVE MARTINGALE  
INEQUALITIES

Marius Junge and Quanhua Xu

We determine the optimal orders for the best constants in the non- 
commutative
Burkholder-Gundy, Doob and Stein inequalities obtained recently in the
non-commutative martingale theory.


http://front.math.ucdavis.edu/math.OA/0505309

---------------------------------------------------------------

3511. SLE COORDINATE CHANGES

Oded Schramm and  David B. Wilson

The purpose of this note is to describe a framework which unifies  
radial,
chordal and dipolar SLE. When the definition of SLE(\kappa;\rho) is  
extended to
the setting where the force points can be in the interior of the  
domain, radial
SLE(\kappa) becomes chordal SLE(\kappa;\rho), with \rho=\kappa-6, and  
vice
versa. We also write down the martingales describing the Radon-Nykodim
derivative of SLE(\kappa;\rho_1,...,\rho_n) with respect to SLE(\kappa).


http://front.math.ucdavis.edu/math.PR/0505368

---------------------------------------------------------------

3512. A RESOLUTION OF QUANTUM DYNAMICAL SEMIGROUPS

Anilesh Mohari

We consider a class of quantum dissipative systems governed by a one
parameter completely positive maps on a von-Neumann algebra. We  
introduce a
notion of recurrent and metastable projections for the dynamics and  
prove that
the unit operator can be decomposed into orthogonal projections where  
each
projections are recurrent or metastable for the dynamics.


http://front.math.ucdavis.edu/math.OA/0505384

---------------------------------------------------------------

3513. A NETWORK ANALYSIS OF COMMITTEES IN THE UNITED STATES HOUSE OF   
REPRESENTATIVES

Mason A. Porter and  Peter J. Mucha and  M.E.J. Newman and  and Casey  
M. Warmbrand

Network theory provides a powerful tool for the representation and  
analysis
of complex systems of interacting agents. Here we investigate the  
United States
House of Representatives network of committees and subcommittees, with
committees connected according to ``interlocks'' or common  
membership. Analysis
of this network reveals clearly the strong links between different  
committees,
as well as the intrinsic hierarchical structure within the House as a  
whole. We
show that network theory, combined with the analysis of roll call  
votes using
singular value decomposition, successfully uncovers political and
organizational correlations between committees in the House without  
the need to
incorporate other political information.


http://front.math.ucdavis.edu/nlin.AO/0505043

---------------------------------------------------------------

3514. SOME RANDOM TIMES AND MARTINGALES ASSOCIATED WITH $BES_{0} 
(\DELTA)$  PROCESSES $(0<\DELTA<2)$

Ashkan Nikeghbali

In this paper, we study Bessel processes of dimension $\delta\equiv2 
(1-\mu)$,
with $0<\delta<2$, and some related martingales and random times. Our  
approach
is based on martingale techniques and the general theory of stochastic
processes (unlike the usual approach based on excursion theory),  
although for
$0<\delta<1$, these processes are even not semimartingales. The last  
time
before 1 when a Bessel process hits 0, called $g_{\mu}$, plays a key  
role in
our study: we characterize its conditional distribution and extend Paul
L\'{e}vy's arc sine law and a related result of Jeulin about the  
standard
Brownian Motion. We also introduce some remarkable families of  
martingales
related to the Bessel process, thus obtaining in some cases a one  
parameter
extension of some results of Az\'{e}ma and Yor in the Brownian setting:
martingales which have the same set of zeros as the Bessel process  
and which
satisfy the stopping theorem for $g_{\mu}$, a one parameter extension of
Az\'{e}ma's second martingale, etc. Throughout our study, the local  
time of the
Bessel process also plays a central role and we shall establish some  
of its
elementary properties.


http://front.math.ucdavis.edu/math.PR/0505423

---------------------------------------------------------------

3515. ON A FAST, ROBUST ESTIMATOR OF THE MODE: COMPARISONS TO OTHER  
ROBUST  ESTIMATORS WITH APPLICATIONS

David R. Bickel and Rudolf Fruehwirth

Advances in computing power enable more widespread use of the mode,  
which is
a natural measure of central tendency since, as the most probable  
value, it is
not influenced by the tails in the distribution. The properties of the
half-sample mode, which is a simple and fast estimator of the mode of a
continuous distribution, are studied. The half-sample mode is less  
sensitive to
outliers than most other estimators of location, including many other  
low-bias
estimators of the mode. Its breakdown point is one half, equal to  
that of the
median. However, because of its finite rejection point, the half- 
sample mode is
much less sensitive to outliers that are all either greater or less  
than the
other values of the sample. This is confirmed by applying the mode  
estimator
and the median to samples drawn from normal, lognormal, and Pareto
distributions contaminated by outliers. It is also shown that the  
half-sample
mode, in combination with a robust scale estimator, is a highly  
robust starting
point for iterative robust location estimators such as Huber's M- 
estimator. The
half-sample mode can easily be generalized to modal intervals  
containing more
or less than half of the sample. An application of such an estimator  
to the
finding of collision points in high-energy proton-proton interactions is
presented.


http://front.math.ucdavis.edu/math.ST/0505419


From pas at www.economia.unimi.it  Thu Sep  1 17:51:54 2005
From: pas at www.economia.unimi.it (pas@www.economia.unimi.it)
Date: Thu Sep  1 18:00:35 2005
Subject: [Pas] Probability Abstracts 88
Message-ID: <E268CCF4-456F-4C80-A9E4-705BD9725E3B@unimi.it>

                         September 1, 2005

                             Letter 88

         Probability Abstract Service

  ( http://www.economia.unimi.it/PAS )
---------------------------------------------------------------

3516. OPTIMAL LONG TERM INVESTMENT MODEL WITH MEMORY

Akihiko Inoue and Yumiharu Nakano

We consider an investment model with memory in which the prices of n  
risky
assets are driven by an n-dimensional Gaussian process with stationary
increments that is different from Brownian motion. The driving  
process consists
of n independent components, and each component is characterized by two
parameters describing the memory. For the model, we explicitly solve the
problem of maximizing the expected growth rate as well as that of  
maximizing
the probability of overperforming a given benchmark.


http://front.math.ucdavis.edu/math.PR/0506621

---------------------------------------------------------------

3517. GRADIENT BOUNDS FOR SOLUTIONS OF ELLIPTIC AND PARABOLIC EQUATIONS

Vladimir I. Bogachev and  Giuseppe Da Prato and  Michael R\"ockner  
and Zeev  Sobol

Let $L$ be a second order elliptic operator on $R^d$ with a constant
diffusion matrix and a dissipative (in a weak sense) drift $b \in L^p_ 
{loc}$
with some $p>d$.
   We assume that $L$ possesses a Lyapunov function, but no local  
boundedness of
$b$ is assumed. It is known that then there exists a unique  
probability measure
$\mu$ satisfying the equation $L^*\mu=0$ and that the closure of $L$ in
$L^1(\mu)$ generates a Markov semigroup $\{T_t\}_{t\ge 0}$ with the  
resolvent
$\{G_\lambda\}_{\lambda > 0}$.
   We prove that, for any Lipschitzian function $f\in L^1(\mu)$ and all
$t,\lambda>0$, the functions $T_tf$ and $G_\lambda f$ are  
Lipschitzian and
|\nabla T_tf(x)| \leq T_t|\nabla f|(x) and |\nabla G_\lambda f(x)| \leq
\frac{1}{\lambda} G_\lambda |\nabla f|(x).
   An analogous result is proved in the parabolic case.


http://front.math.ucdavis.edu/math.PR/0507079

---------------------------------------------------------------

3518. THE KINETIC LIMIT OF A SYSTEM OF COAGULATING PLANAR BROWNIAN  
PARTICLES

Alan Hammond and  Fraydoun Rezakhanlou

We study a model of mass-bearing coagulating planar Brownian particles.
Coagulation is prone to occur when two particles become within a  
distance of
order $\epsilon$. We assume that the initial number of particles is  
of the
order of $| \log \epsilon |. Under suitable assumptions on the initial
distribution of particles and the microscopic coagulation  
propensities, we show
that the macroscopic particle densities satisfy a Smoluchowski-type  
equation.


http://front.math.ucdavis.edu/math.PR/0507522

---------------------------------------------------------------

3519. WEAK CONVERGENCE OF THE SCALED MEDIAN OF INDEPENDENT BROWNIAN  
MOTIONS

Jason Swanson

We consider the median of n independent Brownian motions, and show  
that this
process, when properly scaled, converges weakly to a centered  
Gaussian process.
The chief difficulty is establishing tightness, which is proved  
through direct
estimates on the increments of the median process. An explicit  
formula is given
for the covariance function of the limit process. The limit process  
is also
shown to be Holder continuous with exponent gamma for all gamma < 1/4.


http://front.math.ucdavis.edu/math.PR/0507524

---------------------------------------------------------------

3520. CONCENTRATION INEQUALITIES WITH EXCHANGEABLE PAIRS (PH.D. THESIS)

Sourav Chatterjee

The purpose of this dissertation is to introduce a version of Stein's  
method
of exchangeable pairs to solve problems in measure concentration. We
specifically target systems of dependent random variables, since that  
is where
the power of Stein's method is fully realized. Because the theory is  
quite
abstract, we have tried to put in as many examples as possible. Some  
of the
highlighted applications are as follows: (a) We shall find an easily  
verifiable
condition under which a popular heuristic technique originating from  
physics,
known as the ``mean field equations'' method, is valid. No such  
condition is
currently known. (b) We shall present a way of using couplings to derive
concentration inequalities. Although couplings are routinely used for  
proving
decay of correlations, no method for using couplings to derive  
concentration
bounds is available in the literature. This will be used to obtain (c)
concentration inequalities with explicit constants under Dobrushin's  
condition
of weak dependence. (d) We shall give a method for obtaining  
concentration of
Haar measures using convergence rates of related random walks on  
groups. Using
this technique and one of the numerous available results about rates of
convergence of random walks, we will then prove (e) a quantitative  
version of
Voiculescu's celebrated connection between random matrix theory and free
probability.


http://front.math.ucdavis.edu/math.PR/0507526

---------------------------------------------------------------

3521. A GENERALIZATION OF STATIONARY AR(1) SCHEMES

S Satheesh and  E Sandhya and S Sherly

Here we develop a first order autoregressive model {Xn} that is  
marginally
stationary where Xn is the sum/ extreme of k i.i.d observations. We  
prove that
stationary solutions to these models are either semi- selfdecomposable/
extreme-semi-selfdecomposable or, sum/ extreme stable with respect to  
Harris
distribution.


http://front.math.ucdavis.edu/math.PR/0507535

---------------------------------------------------------------

3522. ON PATHWISE UNIQUENESS FOR STOCHASTIC HEAT EQUATIONS WITH NON- 
LIPSCHITZ  COEFFICIENTS

Leonid Mytnik and  Edwin Perkins and  Anja Sturm

We consider the existence and pathwise uniqueness of the stochastic heat
equation with a multiplicative colored noise term on IR^d for d  
greater or
equal to 1. We focus on the case of non-Lipschitz noise coefficients and
singular spatial noise correlations. In the course of the proof a new  
result on
Hoelder continuity of the solutions near zero is established.


http://front.math.ucdavis.edu/math.PR/0507545

---------------------------------------------------------------

3523. THE DISTRIBUTION OF THE MINIMUM HEIGHT AMONG PIVOTAL SITES IN  
CRITICAL  TWO-DIMENSIONAL PERCOLATION

Gregory J. Morrow and  Yu Zhang

Let L_n denote the lowest crossing of the 2n \times 2n square box B(n)
centered at the origin for critical site percolation on Z^2 or  
critical site
percolation on the triangular lattice imbedded in Z^2, and denote by  
Q_n the
set of pivotal sites along this crossing. On the event that a pivotal  
site
exists, denote the minimum height that a pivotal site attains above  
the bottom
of B(n) by M_n:= min{m:(x,-n+m)\in Q_n for some -n\le x\le n}. Else,  
define M_n
= 2n. We prove that P(M_n < m) \asymp m/n, uniformly for 1\le m\le n.  
This
relation extends Theorem 1 of van den Berg and Jarai (2003) who  
handle the
corresponding distribution for the lowest crossing in a slightly  
different
context. As a corollary we establish the asymptotic distribution of  
the minimum
height of the set of cut points of a certain chordal SLE_6 in the  
unit square
of C.


http://front.math.ucdavis.edu/math.PR/0507566

---------------------------------------------------------------

3524. ON COMPLETE CHARACTERIZATION OF COEFFICIENTS OF A.E.  
CONVERGING  ORTHOGONAL SERIES

Adam Paszkiewicz

We characterize sequences of numbers $(a_n)$ such that $\sum_{n\geq 1}
a_n\Phi_n$ converges a.e. for any orthonormal system $(\Phi_n)$ in any
$L_2$-space. In our criterion, we use the set $B =\{\sum_{m\geq n} | 
a_m|^2;
n\geq 1\}$ and its information function $$h_B(t) = -\log_3(\beta- 
\alpha)$$ for
$t\in (\alpha, \beta]$, $[\alpha, \beta]\cap B =\{\alpha, \beta\}.$


http://front.math.ucdavis.edu/math.AP/0507568

---------------------------------------------------------------

3525. LIMIT THEOREMS FOR WEIGHTED SAMPLES WITH APPLICATIONS TO  
SEQUENTIAL  MONTE CARLO METHODS

R. Douc (\'Ecole Polytechnique and  Palaiseau) and  France E.  
Moulines  (\'Ecole Nationale Sup\'erieure des T\'el\'ecommunications,  
Paris)

In the last decade, sequential Monte-Carlo methods (SMC) emerged as a  
key
tool in computational statistics. These algorithms approximate a  
sequence of
distributions by a sequence of weighted empirical measures associated  
to a
weighted population of particles. These particles and weights are  
generated
recursively according to elementary transformations: mutation and  
selection.
Examples of applications include the sequential Monte-Carlo  
techniques to solve
optimal non-linear filtering problems in state-space models, molecular
simulation, genetic optimization, etc.
   Despite many theoretical advances the asymptotic property of these
approximations remains of course a question of central interest. In  
this paper,
we analyze sequential Monte Carlo methods from an asymptotic  
perspective, that
is, we establish law of large numbers and invariance principle as the  
number of
particles gets large. We introduce the concepts of "weighted sample"
consistency and asymptotic normality, and derive conditions under  
which the
mutation and the selection procedure used in the sequential Monte-Carlo
build-up preserve these properties. To illustrate our findings, we  
analyze SMC
algorithms to approximate the filtering distribution in state-space  
models. We
show how our techniques allow to relax restrictive technical  
conditions used in
previously reported works and provide grounds to analyze more  
sophisticated
sequential sampling strategies.


http://front.math.ucdavis.edu/math.ST/0507042

---------------------------------------------------------------

3526. THE CONTACT PROCESS SEEN FROM A TYPICAL INFECTED SITE

J.M. Swart

This paper considers contact processes on general lattices. Assuming  
that the
expected number of infected sites grows subexponentially, it is shown  
that the
configuration as seen from a typical (`Palmed') infected site at an
exponentially distributed time converges, as time tends to infinity,  
to the
upper invariant law conditioned on the origin being infected. The  
assumption
that the expected number of infected sites grows subexponentially is  
shown to
be satisfied if the lattice has subexponential growth and the  
infection rates
satisfy an exponential moment condition.


http://front.math.ucdavis.edu/math.PR/0507578

---------------------------------------------------------------

3527. ESTIMATES OF POTENTIAL KERNEL AND HARNACK'S INEQUALITY FOR  
ANISOTROPIC  FRACTIONAL LAPLACIAN

Krzysztof Bogdan and Pawe{\l} Sztonyk

We characterize those homogeneous translation invariant symmetric non- 
local
operators with positive maximum principle whose harmonic functions  
satisfy
Harnack's inequality. We also estimate the corresponding semigroup  
and the
potential kernel.


http://front.math.ucdavis.edu/math.PR/0507579

---------------------------------------------------------------

3528. INTERNAL DIFFUSION LIMITED AGGREGATION ON DISCRETE GROUPS  
HAVING  EXPONENTIAL GROWTH

Sebastien Blachere and Sara Brofferio

The Internal Diffusion Limited Aggregation has been introduced by  
Diaconis
and Fulton in 1991. It is a growth model defined on an infinite set and
associated to a Markov chain on this set. We focus here on sets which  
are
finitely generated groups with exponential growth. We prove a shape  
theorem for
the Internal DLA on such groups associated to symmetric random walks.  
For that
purpose, we introduce a new distance associated to the Green  
function, which
happens to have some interesting properties. In the case of  
homogeneous trees,
we also get the right order for the fluctuations of that model around  
its
limiting shape.


http://front.math.ucdavis.edu/math.PR/0507582

---------------------------------------------------------------

3529. GEOMETRIC CHARACTERISATION OF INTERMITTENCY IN THE PARABOLIC  
ANDERSON  MODEL

J. Gaertner and  W. Koenig and  S. Molchanov

We consider the parabolic Anderson problem $\partial_t u =\Delta u+\xi 
(x) u$
on $\R_+\times \Z^d$ with localized initial condition $u(0,x)=\delta_0 
(x)$ and
random i.i.d. potential $\xi$. Under the assumption that the  
distribution of
$\xi(0)$ lies in the vicinity of, or beyond, the double-exponential
distribution, we prove the following geometric characterisation of
intermittency: with probability one, as $t\to\infty$, the overwhelming
contribution to the total mass $\sum_x u(t,x)$ comes from a slowly  
increasing
number of islands which are located far from each other. These  
islands are
local regions of those high exceedances of the field $\xi$ in a box  
with radius
$t\log^2t$ for which the (local) principal Dirichlet eigenvalue of  
the random
operator $\Delta+\xi$ is close to maximal. We also prove that the  
shape of
$\xi$ in these regions is non-random and that $u(t,\cdot)$ is close  
to the
corresponding positive eigenfunction. This is the geometric picture  
suggested
by localization theory for the Anderson Hamiltonian.


http://front.math.ucdavis.edu/math.PR/0507585

---------------------------------------------------------------

3530. COAGULATION-FRAGMENTATION DUALITY, POISSON-DIRICHLET  
DISTRIBUTIONS AND  RANDOM RECURSIVE TREES

Rui Dong and  Christina Goldschmidt and James B. Martin

In this paper we give a new example of duality between fragmentation and
coagulation operators. Consider the space of partitions of mass (that  
is,
decreasing sequences of non-negative real numbers whose sum is 1) and  
the
two-parameter family of Poisson-Dirichlet distributions PD 
(alpha,theta), taking
values in this space. We introduce families of random fragmentation and
coagulation operators, Frag_{alpha} and Coag_{alpha,theta}  
respectively, with
the following property: if the input to Frag_{alpha} has PD(alpha,theta)
distribution then the output has PD(alpha,theta+1) distribution,  
while the
reverse is true for Coag_{alpha,theta}. This result may be proved  
using a
subordinator representation, and provides a companion set of  
relations to those
of Pitman between PD(alpha,theta) and PD(alpha*beta,theta). Repeated
application of the Frag_{alpha} operators gives rise to a family of
fragmentation chains. We show that these Markov chains can be encoded
natuarally by certain random recursive trees, and use this  
representation to
give an alternative and more concrete proof of the coagulation- 
fragmentation
duality.


http://front.math.ucdavis.edu/math.PR/0507591

---------------------------------------------------------------

3531. EXPLICIT INVARIANT MEASURES FOR PRODUCTS OF RANDOM MATRICES

Jens Marklof and  Yves Tourigny and  Lech Wolowski

We construct explicit invariant measures for a family of infinite  
products of
random, independent, identically-distributed elements of SL(2,C). The  
matrices
in the product are such that one entry is gamma-distributed along a  
ray in the
complex plane. When the ray is the positive real axis, the products  
are those
associated with a continued fraction studied by Letac and Seshadri  
[Z. Wahr.
Verw. Geb. 62 (1983) 485-489], who showed that the distribution of the
continued fraction is a generalised inverse Gaussian. We extend this  
result by
finding the distribution for an arbitrary ray in the complex right- 
half plane,
and thus compute the corresponding Lyapunov exponent explicitly. When  
the ray
lies on the imaginary axis, the matrices in the infinite product  
coincide with
the transfer matrices associated with a one-dimensional discrete  
Schroedinger
operator with a random, gamma-distributed potential. Hence, the explicit
knowledge of the Lyapunov exponent may be used to estimate the  
(exponential)
rate of localisation of the eigenstates.


http://front.math.ucdavis.edu/math-ph/0507069

---------------------------------------------------------------

3532. INTER-ARRIVAL TIME DISTRIBUTION FOR THE NON-HOMOGENEOUS POISSON  
PROCESS

Gleb Yakovlev and  John B. Rundle and  Robert Shcherbakov and  and  
Donald L.  Turcotte

We derive an analytical expression of the inter-arrival time  
distribution for
a non-homogeneous Poisson process (NHPP). This expression is exact  
and is
applicable to any time interval, finite or infinite. As an  
illustration, we
present simulation results for three different intensity functions.


http://front.math.ucdavis.edu/cond-mat/0507657

---------------------------------------------------------------

3533. A FAST ALGORITHM FOR SIMULATING THE CHORDAL SCHRAMM-LOEWNER  
EVOLUTION

Tom Kennedy

The Schramm-Loewner evolution (SLE) can be simulated by dividing the  
time
interval into N subintervals and approximating the random conformal  
map of the
SLE by the composition of N random, but relatively simple, conformal  
maps. In
the usual implementation the time required to compute a single point  
on the SLE
curve is O(N). We give an algorithm for which the time to compute a  
single
point is O(N^p) with p<1. Simulations with kappa=8/3 and kappa=6 both  
give a
value of p of approximately 0.4.


http://front.math.ucdavis.edu/math.PR/0508002

---------------------------------------------------------------

3534. ASYMPTOTIC ANALYSIS OF MULTISCALE APPROXIMATIONS TO REACTION  
NETWORKS

Karen Ball and  Tom Kurtz and  Lea Popovic and  and Greg Rempala

A reaction network is a chemical system involving multiple reactions and
chemical species. Stochastic models of such networks treat the system  
as a
continuous time Markov chain on the number of molecules of each  
species with
reactions as possible transitions of the chain. In many cases of  
biological
interest some of the chemical species in the network are present in much
greater abundance than others and reaction rate constants can vary  
over several
orders of magnitude. We consider approaches to approximation of such  
models
that take the multiscale nature of the system into account. Our  
primary example
is a model of a cell's viral infection for which we apply a  
combination of
averaging and law of large number arguments to show that the ``slow''  
component
of the model can be approximated by a deterministic equation and to
characterize the asymptotic distribution of the ``fast'' components.  
The main
goal is to illustrate techniques that can be used to reduce the  
dimensionality
of much more complex models.


http://front.math.ucdavis.edu/math.PR/0508015

---------------------------------------------------------------

3535. A NECESSARY CONDITION FOR THE UNIQUENESS OF THE STATIONARY  
STATE OF A  MARKOV SYSTEM

Ivan Werner

We continue the study of Markov systems started in \cite{Wer1}. In this
paper, we prove a generalization of Breiman's strong low of large  
numbers
\cite{Br} which implies a necessary condition for the uniqueness of the
stationary state of a Markov system.


http://front.math.ucdavis.edu/math.PR/0508054

---------------------------------------------------------------

3536. QUANTUM FILTERING: A REFERENCE PROBABILITY APPROACH

Luc Bouten and Ramon van Handel

These notes are intended as an introduction to noncommutative (quantum)
filtering theory. An introduction to quantum probability theory is  
given,
focusing on the spectral theorem and the conditional expectation as  
the least
squares estimate, and culminating in the construction of Wiener and  
Poisson
processes on the Fock space. Next we describe the Hudson- 
Parthasarathy quantum
Ito calculus and its use in the modelling of physical systems.  
Finally, we use
a reference probability method to obtain quantum filtering equations,  
in the
Belavkin-Zakai (unnormalized) form, for several system-observation  
models from
quantum optics. The normalized (Belavkin-Kushner-Stratonovich) form  
is obtained
through a noncommutative analogue of the Kallianpur-Striebel formula.


http://front.math.ucdavis.edu/math-ph/0508006

---------------------------------------------------------------

3537. POSITION PLAY IN CAROM BILLIARDS AS A MARKOV PROCESS

Mathieu Bouville

Using certain techniques a billiards player can have long series of easy
shots --each shot leading to another easy shot-- and very high  
scores. As the
usual model for carom billiards assumes a Bernoulli process which  
does not
account for such correlations, it cannot capture this important  
feature of the
game. Modelling carom billiards as a Markov process, the probability  
to make a
shot can be made to depend on the previous shot. The improved  
agreement with
data is an indication that a Markov process indeed captures the  
effects of
position play better. Moreover it is possible to quantify how much a  
player
plays position. Given two players with the same average, one can tell  
the good
shot-maker from the good position player. This can be useful for  
players (and
their coaches) to evaluate their strengths and weaknesses.


http://front.math.ucdavis.edu/math.PR/0508089

---------------------------------------------------------------

3538. GEODESICS IN FIRST PASSAGE PERCOLATION

Christopher Hoffman

We consider a wide class of ergodic first passage percolation  
processes on
Z^2 and prove that there exist at least four one-sided geodesics a.s.  
We also
show that coexistence is possible with positive probability in a four  
color
Richardson's growth model. This improves earlier results of Haggstrom  
and
Pemantle, Garet and Marchand, and Hoffman who proved that first passage
percolation has at least two geodesics and that coexistence is  
possible in a
two color Richardson's growth model.


http://front.math.ucdavis.edu/math.PR/0508114

---------------------------------------------------------------

3539. LIMIT SHAPES AND THE COMPLEX BURGERS EQUATION

Richard Kenyon and Andrei Okounkov

In this paper we study surfaces in R^3 that arise as limit shapes in  
a class
of random surface models arising from dimer models. The limit shapes are
minimizers of a surface tension functional, that is, they minimize,  
for fixed
boundary conditions, the integral of a quantity (the surface tension)  
depending
only on the slope of the surface. The surface tension as a function  
of the
slope has singularities and is not strictly convex, which leads to  
formation of
facets and edges in the limit shapes.
   We find a change of variables that reduces the Euler-Lagrange  
equation for
the variational problem to the complex inviscid Burgers equation  
(complex Hopf
equation). The equation can thus be solved in terms of an arbitrary  
holomorphic
function, which is somewhat similar in spirit to Weierstrass  
parametrization of
minimal surfaces. We further show that for a natural dense set of  
boundary
conditions, the holomorphic function in question is, in fact,  
algebraic. The
tools of algebraic geometry can thus be brought in to study the the  
minimizers
and, especially, the formation of their singularities. This is  
illustrated by
several explicitly computed examples.


http://front.math.ucdavis.edu/math-ph/0507007

---------------------------------------------------------------

3540. A REFINEMENT OF THE EULERIAN NUMBERS, AND THE JOINT  
DISTRIBUTION OF  $\PI(1)$ AND DES($\PI$) IN $S_N$

Mark Conger

Given a permutation $\pi$ chosen uniformly from $S_n$, we explore the  
joint
distribution of $\pi(1)$ and the number of descents in $\pi$. We  
obtain a
formula for the number of permutations with $\des(\pi)=d$ and $\pi(1) 
=k$, and
use it to show that if $\des(\pi)$ is fixed at $d$, then the expected  
value of
$\pi(1)$ is $d+1$. We go on to derive generating functions for the joint
distribution, show that it is unimodal if viewed correctly, and show  
that when
$d$ is small the distribution of $\pi(1)$ among the permutations with  
$d$
descents is approximately geometric. Applications to Stein's method  
and the
Neggers-Stanley problem are presented.


http://front.math.ucdavis.edu/math.CO/0508112

---------------------------------------------------------------

3541. COHERENT PERMUTATIONS WITH DESCENT STATISTIC AND THE BOUNDARY  
PROBLEM  FOR THE GRAPH OF ZIGZAG DIAGRAMS

Alexander Gnedin and Grigori Olshanski

The graph of zigzag diagrams is a close relative of Young's lattice. The
boundary problem for this graph amounts to describing coherent random
permutations with descent-set statistic, and is also related to certain
positive characters on the algebra of quasi-symmetric functions. We  
establish
connections to some further relatives of Young's lattice and solve  
the boundary
problem by reducing it to the classification of spreadable total  
orders on
integers, as recently obtained by Jacka and Warren.


http://front.math.ucdavis.edu/math.CO/0508131

---------------------------------------------------------------

3542. RAINBOW HAMILTON CYCLES IN RANDOM REGULAR GRAPHS

Svante Janson and Nicholas Wormald

A rainbow subgraph of an edge-coloured graph has all edges of distinct
colours. A random d-regular graph with d even, and having edges coloured
randomly with d/2 of each of n colours, has a rainbow Hamilton cycle  
with
probability tending to 1 as n tends to infinity, provided d is at  
least 8.


http://front.math.ucdavis.edu/math.CO/0508145

---------------------------------------------------------------

3543. BOUNDS FOR CRITICAL VALUES OF THE BAK-SNEPPEN MODEL ON  
TRANSITIVE GRAPHS

Alexis Gillett and  Ronald Meester and  Misja Nuyens

We study the Bak-Sneppen model on locally finite transitive graphs $G 
$, in
particular on $\mathbb{Z}^d$ and on $T_{\Delta}$, the regular tree  
with common
degree $\Delta$. We show that the avalanches of the Bak-Sneppen model  
dominate
independent site percolation, in a sense to be made precise. Together  
with the
fact that avalanches of the Bak-Sneppen model are dominated by a simple
branching process, this yields upper and lower bounds for the  
critical value
$p_c^{BS}(G)$ of the Bak-Sneppen model. Our main results state that
$\frac{1}{\Delta+1} \le p_c^{BS}(T_\Delta) \le \frac{1}{\Delta -1}$,  
and that
$\frac{1}{2d+1}\leq p_c^{BS}(\mathbb{Z}^d)\leq \frac{1}{2d}+
\frac{1}{(2d)^2}+O\big(d^{-3}\big)$, as $d\to\infty$.


http://front.math.ucdavis.edu/math.PR/0508167

---------------------------------------------------------------

3544. ON A SIMPLE STRATEGY WEAKLY FORCING THE STRONG LAW OF LARGE  
NUMBERS IN  THE BOUNDED FORECASTING GAME

Masayuki Kumon and Akimichi Takemura

In the framework of the game-theoretic probability of Shafer and Vovk  
(2001)
it is of basic importance to construct an explicit strategy weakly  
forcing the
strong law of large numbers (SLLN) in the bounded forecasting game.  
We present
a simple finite-memory strategy based on the past average of  
Reality's moves,
which weakly forces the strong law of large numbers with the  
convergence rate
of $O(\sqrt{\log n/n})$. We also give a detailed analysis of the  
paths of
Skeptic's capital process for the case of the fair-coin game when our  
strategy
is used. We show that if Reality violates SLLN, then the exponential  
growth
rate of Skeptic's capital process is explicitly described in terms of  
the
Kullback divergence between the average of Reality's moves when she  
violates
SLLN and the average when she observes SLLN.


http://front.math.ucdavis.edu/math.PR/0508190

---------------------------------------------------------------

3545. HARMONICITY OF GIBBS MEASURES

Chris Connell and Roman Muchnik

In this paper we extend the construction of random walks with a  
prescribed
Poisson boundary to the case of measures in the class of a  
generalized Gibbs
state. The price for dropping the $\alpha$-quasiconformal assumptions  
is that
we must restrict our attention to CAT($-\kappa$) groups. Apart from  
the new
estimates required, we prove a new approximation scheme to provide a  
positive
basis for positive functions in a metric measure space.


http://front.math.ucdavis.edu/math.GR/0507033

---------------------------------------------------------------

3546. LOGICAL STRUCTURE OF PHYSICAL PROBABILITY ASSERTIONS

Joseph F. Johnson

A modification and generalisation of von Plato's fix of the frequency  
theory
of probability is presented. It is thermodynamic in nature. Von Plato  
already
fixed the logical circle in the frequency theory, we generalise his  
results to
not necessarily ergodic systems of classical and quantum mechanics.  
This turns
out to be precisely what is needed for the problem of Quantum  
Measurement and
the problem of induction.


http://front.math.ucdavis.edu/quant-ph/0508059

---------------------------------------------------------------

3547. A SIMPLE INVARIANCE THEOREM

Sourav Chatterjee

We present a simple extension of Lindeberg's argument for the Central  
Limit
Theorem to get a general invariance result. We apply the technique to  
prove
results from random matrix theory, spin glasses, and maxima of random  
fields.


http://front.math.ucdavis.edu/math.PR/0508213

---------------------------------------------------------------

3548. NORMAL APPROXIMATIONS FOR DESCENTS AND INVERSIONS OF  
PERMUTATIONS OF  MULTISETS

Mark Conger and D. Viswanath

Normal approximations for descents and inversions of permutations of  
the set
$\{1,2,...,n\}$ are well known. A number of sequences that occur in  
practice,
such as the human genome and other genomes, contain many repeated  
elements.
Motivated by such examples, we consider the number of inversions of a
permutation $\pi(1), \pi(2),...,\pi(n)$ of a multiset with $n$  
elements, which
is the number of pairs $(i,j)$ with $1\leq i < j \leq n$ and $\pi(i)> 
\pi(j)$.
The number of descents is the number of $i$ in the range $1\leq i < n 
$ such
that $\pi(i) > \pi(i+1)$. We prove that, appropriately normalized, the
distribution of both inversions and descents of a random permutation  
of the
multiset approaches the normal distribution as $n\to\infty$, provided  
that the
permutation is equally likely to be any possible permutation of the  
multiset
and no element occurs more than $\alpha n$ times in the multiset for  
a fixed
$\alpha$ with $0<\alpha < 1$. Both normal approximation theorems are  
proved
using the size biased version of Stein's method of auxiliary  
randomization and
are accompanied by error bounds.


http://front.math.ucdavis.edu/math.PR/0508242

---------------------------------------------------------------

3549. LAWS OF THE ITERATED LOGARITHM FOR \ALPHA-TIME BROWNIAN MOTION

Erkan Nanw

We introduce a class of iterated processes called $\alpha$-time Brownian
motion for $0<\alpha \leq 2$. These are obtained by taking Brownian  
motion and
replacing the time parameter with a symmetric $\alpha$-stable  
process. We prove
a Chung-type law of the iterated logarithm (LIL) for these processes  
which is a
generalization of LIL proved in \cite{hu} for iterated Brownian  
motion. When
$\alpha =1$ it takes the following form $$ \liminf_{T\to\infty}T^ 
{-1/2}(\log
\log T) \sup_{0\leq t\leq T}|Z_{t}|=\pi^{2}\sqrt{\lambda_{1}} a.s. $$  
where
$\lambda_{1}$ is the first eigenvalue for the Cauchy process in the  
interval
$[-1,1].$ We also define the local time $L^{*}(x,t)$ and range $R^{*} 
(t)=|\{x:
Z(s)=x \text{for some} s\leq t\}|$ for these processes for $1<\alpha  
<2$. We
prove that there are universal constants $c_{R},c_{L}\in (0,\infty) $  
such that
$$ \limsup_{t\to\infty}\frac{R^{*}(t)}{(t/\log \log t)^{1/2\alpha} 
\log \log t}=
c_{R} a.s. $$ $$
   \liminf_{t\to\infty} \frac{\sup_{x\in \RR{R}}L^{*}(x,t)}{(t/\log \log
t)^{1-1/2\alpha}}= c_{L} a.s. $$


http://front.math.ucdavis.edu/math.PR/0508261

---------------------------------------------------------------

3550. HIGHER ORDER PDE'S AND ITERATED PROCESSES

Erkan nane

We introduce a class of stochastic processes based on symmetric
$\alpha$-stable processes, for $\alpha \in (0,2]$ rational.
These are obtained by taking Markov processes and replacing the time  
parameter
with the modulus of a symmetric $\alpha$-stable process. We call them
$\alpha$-time processes. They generalize Brownian time processes  
studied in
\cite{allouba1, allouba2, allouba3}, and they introduce new interesting
examples. We establish the connection of
$\alpha-$time processes to some higher order PDE's. We also study the  
exit
problem for $\alpha$-time processes as they exit regular domains and  
connect
them to elliptic PDE's. We also obtain the PDE connection of  
subordinate killed
Brownian motion in bounded domains of regular boundary.


http://front.math.ucdavis.edu/math.PR/0508262

---------------------------------------------------------------

3551. THE ARITHMETIC OF DISTRIBUTIONS IN FREE PROBABILITY THEORY

G. Chistyakov and F. G\"otze

We give a new approach to the definition of additive and  
multiplicative free
convolutions which is based on the theory of Nevanlinna and of Schur  
functions.
We consider the set of probability distributions as a semigroup M  
equipped with
the operation of free convolution and prove a Khintchine type theorem  
for
factorization of elements of this semigroup. Any element of M  
contains either
indecomposable factors or it belongs to a class, say I_0, of  
distributions
without indecomposable factors. In contrast to the classical convolution
semigroup in the free additive and multiplicative convolution  
semigroups the
class I_0 consists of units (i.e. Dirac measures) only. Furthermore  
we show
that the set of indecomposable elements is dense in M.


http://front.math.ucdavis.edu/math.OA/0508245

---------------------------------------------------------------

3552. AUTOMATIC FILTERS FOR THE DETECTION OF COHERENT STRUCTURE IN   
SPATIOTEMPORAL SYSTEMS

Cosma Rohilla Shalizi and  Robert Haslinger and  Jean-Baptiste  
Rouquier and   Kristina Lisa Klinkner, Cristopher Moore

Most current methods for identifying coherent structures in
spatially-extended systems rely on prior information about the form  
which those
structures take. Here we present two new approaches to automatically  
filter the
changing configurations of spatial dynamical systems and extract  
coherent
structures. One, local sensitivity filtering, is a modification of  
the local
Lyapunov exponent approach suitable to cellular automata and other  
discrete
spatial systems. The other, local statistical complexity filtering,  
calculates
the amount of information needed for optimal prediction of the system's
behavior in the vicinity of a given point. By examining the changing
spatiotemporal distributions of these quantities, we can find the  
coherent
structures in a variety of pattern-forming cellular automata, without  
needing
to guess or postulate the form of that structure. We apply both  
filters to
elementary and cyclical cellular automata (ECA and CCA) and find that  
they
readily identify particles, domains and other more complicated  
structures. We
compare the results from ECA with earlier ones based upon the theory  
of formal
languages, and the results from CCA with a more traditional approach  
based on
an order parameter and free energy. While sensitivity and statistical
complexity are equally adept at uncovering structure, they are based on
different system properties (dynamical and probabilistic,  
respectively), and
provide complementary information.


http://front.math.ucdavis.edu/nlin.CG/0508001

---------------------------------------------------------------

3553. ALMOST SURE RECURRENCE OF THE SIMPLE RANDOM WALK PATH

Itai Benjamini and  Ori Gurel-Gurevich

It is shown that the simple random walk path on a bounded degree graph,
consisting of all vertices visited and edges crossed by the walk, is  
almost
surely a recurrent subgraph.


http://front.math.ucdavis.edu/math.PR/0508270

---------------------------------------------------------------

3554. CONTINUITY OF THE MIXING OPERATOR

Mikhail Kovtun

Mixed distributions are considered as a results of application of a  
linear
operator, which maps mixing measures to mixed measures. The main  
result is a
proof of continuity of this mixing operator. Corollaries for parametric
families of distributions (usually considered in literature) are also
discussed.


http://front.math.ucdavis.edu/math.PR/0508296

---------------------------------------------------------------

3555. EVERY DECISION TREE HAS AN INFLUENTIAL VARIABLE

Ryan O'Donnell and  Michael Saks and  Oded Schramm and  Rocco A.  
Servedio

We prove that for any decision tree calculating a boolean function
$f:\{-1,1\}^n\to\{-1,1\}$, \[ \Var[f] \le \sum_{i=1}^n \delta_i \Inf_i 
(f), \]
where $\delta_i$ is the probability that the $i$th input variable is  
read and
$\Inf_i(f)$ is the influence of the $i$th variable on $f$. The variance,
influence and probability are taken with respect to an arbitrary product
measure on $\{-1,1\}^n$. It follows that the minimum depth of a  
decision tree
calculating a given balanced function is at least the reciprocal of  
the largest
influence of any input variable. Likewise, any balanced boolean  
function with a
decision tree of depth $d$ has a variable with influence at least
$\frac{1}{d}$. The only previous nontrivial lower bound known was $ 
\Omega(d
2^{-d})$. Our inequality has many generalizations, allowing us to prove
influence lower bounds for randomized decision trees, decision trees on
arbitrary product probability spaces, and decision trees with non- 
boolean
outputs. As an application of our results we give a very easy proof  
that the
randomized query complexity of nontrivial monotone graph properties  
is at least
$\Omega(v^{4/3}/p^{1/3})$, where $v$ is the number of vertices and $p  
\leq
\half$ is the critical threshold probability. This supersedes the  
milestone
$\Omega(v^{4/3})$ bound of Hajnal and is sometimes superior to the  
best known
lower bounds of Chakrabarti-Khot and Friedgut-Kahn-Wigderson.


http://front.math.ucdavis.edu/cs.CC/0508071

---------------------------------------------------------------

3556. COMBINATIONS AND MIXTURES OF OPTIMAL POLICIES IN UNICHAIN  
MARKOV  DECISION PROCESSES ARE OPTIMAL

Ronald Ortner

We show that combinations of optimal (stationary) policies in  
unichain Markov
decision processes are optimal. That is, let M be a unichain Markov  
decision
process with state space S, action space A and policies \pi_j^*: S ->  
A (1\leq
j\leq n) with optimal average infinite horizon reward. Then any  
combination \pi
of these policies, where for each state i in S there is a j such that
\pi(i)=\pi_j^*(i), is optimal as well. Furthermore, we prove that any  
mixture
of optimal policies, where at each visit in a state i an arbitrary  
action
\pi_j^*(i) of an optimal policy is chosen, yields optimal average  
reward, too.


http://front.math.ucdavis.edu/math.CO/0508319

---------------------------------------------------------------

3557. CENTRAL LIMIT THEOREMS FOR A CLASS OF IRREDUCIBLE MULTICOLOR  
URN MODELS

Gopal K. Basak and Amites Dasgupta

We take a unified approach to central limit theorems for a class of
irreducible urn models with constant replacement matrix. Depending on  
the
eigenvalue, we consider appropriate linear combinations of the number  
of balls
of different colors. Then under appropriate norming the multivariate
distribution of the weak limits of these linear combinations is  
obtained and
independence and dependence issues are investigated.


http://front.math.ucdavis.edu/math.PR/0507084

---------------------------------------------------------------

3558. A LATTICE SCHEME FOR STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS  
OF  ELLIPTIC TYPE IN DIMENSION $D\GE 4$

Teresa Mart\'inez and Marta Sanz-Sol\'e

We study a stochastic boundary value problem on $(0,1)^d$ of elliptic  
type in
dimension $d\ge 4$, driven by a coloured noise. An approximation  
scheme based
on a suitable discretization of the Laplacian on a lattice of $(0,1)^d 
$ is
presented; we also give the rate of convergence to the original SPDE in
$L^p(\Omega;L^{2}(D))$--norm, for some values of $p$.


http://front.math.ucdavis.edu/math.PR/0508339

---------------------------------------------------------------

3559. THE SCALING LIMIT OF LOOP-ERASED RANDOM WALK IN THREE DIMENSIONS

Gady Kozma

We show that the scaling limit exists and is invariant to dilations and
rotations. We give some tools that might be useful to show universality.


http://front.math.ucdavis.edu/math.PR/0508344

---------------------------------------------------------------

3560. HYDRODYNAMIC LIMIT FLUCTUATIONS OF SUPER-BROWNIAN MOTION WITH A  
STABLE  CATALYST

Klaus Fleischmann and  Peter Moerters and  and Vitali Wachtel

We consider the behaviour of a continuous super-Brownian motion  
catalysed by
a random medium with infinite overall density under the hydrodynamic  
scaling of
mass, time, and space. We show that, in supercritical dimensions, the  
scaled
process converges to a macroscopic heat flow, and the appropriately  
rescaled
random fluctuations around this macroscopic flow are asymptotically  
bounded, in
the sense of log-Laplace transforms, by generalised stable Ornstein- 
Uhlenbeck
processes. The most interesting new effect we observe is the  
occurrence of an
index-jump from a 'Gaussian' situation to stable fluctuations of  
index 1+gamma,
where gamma is an index associated to the medium.


http://front.math.ucdavis.edu/math.PR/0508368

---------------------------------------------------------------

3561. RANDOM ORDERINGS OF THE INTEGERS AND CARD SHUFFLING

Saul Jacka and Jon Warren

In this paper we study random orderings of the integers with a certain
invariance property. We describe all such orders in a simple way. We  
define and
represent random shuffles of a countable set of labels and then give an
interpretation of these orders in terms of a class of generalized riffle
shuffles.


http://front.math.ucdavis.edu/math.PR/0508369

---------------------------------------------------------------

3562. ALMOST SURE CONVERGENCE OF SOLUTIONS TO NON-HOMOGENEOUS  
STOCHASTIC  DIFFERENCE EQUATION

Gregory Berkolaiko and  Alexandra Rodkina

We consider a non-homogeneous nonlinear stochastic difference equation
   X_{n+1} = X_n (1 + f(X_n)\xi_{n+1}) + S_n, and its important  
special case
   X_{n+1} = X_n (1 + \xi_{n+1}) + S_n, both with initial value X_0,  
non-random
decaying free coefficient S_n and independent random variables \xi_n. We
establish results on \as convergence of solutions X_n to zero. The  
necessary
conditions we find tie together certain moments of the noise \xi_n  
and the rate
of decay of S_n. To ascertain sharpness of our conditions we discuss  
some
situations when X_n diverges. We also establish a result concerning  
the rate of
decay of X_n to zero.


http://front.math.ucdavis.edu/math.PR/0508371

---------------------------------------------------------------

3563. ON CONVERGENCE TO EQUILIBRIUM DISTRIBUTION, II. THE WAVE  
EQUATION IN ODD  DIMENSIONS, WITH MIXING

T.V. Dudnikova and  A.I. Komech and  N.E. Ratanov and  Yu.M. Suhov

The paper considers the wave equation, with constant or variable  
coefficients
in $\R^n$, with odd $n\geq 3$. We study the asymptotics of the  
distribution
$\mu_t$ of the random solution at time $t\in\R$ as $t\to\infty$. It  
is assumed
that the initial measure $\mu_0$ has zero mean, translation-invariant
covariance matrices, and finite expected energy density. We also  
assume that
$\mu_0$ satisfies a Rosenblatt- or Ibragimov-Linnik-type space mixing
condition. The main result is the convergence of $\mu_t$ to a  
Gaussian measure
$\mu_\infty$ as $t\to\infty$, which gives a Central Limit Theorem  
(CLT) for the
wave equation. The proof for the case of constant coefficients is  
based on an
analysis of long-time asymptotics of the solution in the Fourier  
representation
and Bernstein's `room-corridor' argument. The case of variable  
coefficients is
treated by using a version of the scattering theory for infinite energy
solutions, based on Vainberg's results on local energy decay.


http://front.math.ucdavis.edu/math-ph/0508039

---------------------------------------------------------------

3564. RANK STATISTICS IN BIOLOGICAL EVOLUTION

E. Ben-Naim and  P.L. Krapivsky

We present a statistical analysis of biological evolution processes.
Specifically, we study the stochastic replication-mutation-death  
model where
the population of a species may grow or shrink by birth or death,  
respectively,
and additionally, mutations lead to the creation of new species. We  
rank the
various species by the chronological order by which they originate.  
The average
population N_k of the kth species decays algebraically with rank, N_k  
~ M^{mu}
k^{-mu}, where M is the average total population. The characteristic  
exponent
mu=(alpha-gamma)/(alpha+beta-gamma)$ depends on alpha, beta, and  
gamma, the
replication, mutation, and death rates. Furthermore, the average  
population P_k
of all descendants of the kth species has a universal algebraic  
behavior, P_k ~
M/k.


http://front.math.ucdavis.edu/q-bio.PE/0508023

---------------------------------------------------------------

3565. CLASSICAL BI-POISSON PROCESS: AN INVERTIBLE QUADRATIC HARNESS

Wlodzimierz Bryc and Jacek Wesolowski

We give an elementary construction of a time-invertible Markov  
process which
is discrete except at one instance. The process is one of the quadratic
harnesses studied in our previous papers and can be regarded as a  
random joint
of two independent Poisson processes.


http://front.math.ucdavis.edu/math.PR/0508383

---------------------------------------------------------------

3566. ROUTING IN POISSON SMALL-WORLD NETWORKS

M. Draief and A. Ganesh

In recent work, Jon Kleinberg considered a small-world network model
consisting of a d-dimensional lattice augmented with shortcuts. The  
probability
of a shortcut being present between two points decays as a power of the
distance between them. Kleinberg studied the efficiency of greedy  
routing
depending on the value of the power. The results were extended to a  
continuum
model by Franceschetti and Meester. In our work, we extend the result  
to more
realistic models constructed from a Poisson point process, wherein  
each point
is connected to all its neighbours within some fixed radius, as well as
possessing random shortcuts to more distant nodes as described above.


http://front.math.ucdavis.edu/math.PR/0508410

---------------------------------------------------------------

3567. BROWNIAN LOCAL MINIMA AND OTHER RANDOM DENSE COUNTABLE SETS

Boris Tsirelson

We compare two examples of random dense countable sets, `Brownian local
minima' and `unordered uniform infinite sample'. They appear to be  
identically
distributed. A framework for such notions is proposed. In addition,  
random
elements of other singular spaces (especially, reals modulo  
rationals) are
considered.


http://front.math.ucdavis.edu/math.PR/0508414

---------------------------------------------------------------

3568. ON THE STRONG CONSISTENCY OF APPROXIMATED M-ESTIMATORS

Djalil Chafai (LSProba and  Upte Umr Inra/Envt 181) and  Didier  
Concordet  (LSProba, Upte Umr Inra/Envt 181)

The aim of this article is to provide a strong consistency Theorem for
approximated M-estimators. It contains both Wald and Pfanzagl type  
results for
maximum likelihood. The proof relies, in particular, on the existence  
of a sort
of contraction of the parameter space which admits the true parameter  
as a
fixed point. In a way, it can be seen as a simplification of ideas of  
Wang and
Pfanzagl, generalised to approximated M-estimators. Proofs are short and
elementary.


http://front.math.ucdavis.edu/math.PR/0507102

---------------------------------------------------------------

3569. ON CONVERGENCE TO EQUILIBRIUM DISTRIBUTION, I. THE KLEIN -  
GORDON  EQUATION WITH MIXING

T.V. Dudnikova and  A.I. Komech and  E.A. Kopylova and  Yu.M. Suhov

Consider the Klein-Gordon equation (KGE) in $\R^n$, $n\ge 2$, with  
constant
or variable coefficients. We study the distribution $\mu_t$ of the  
random
solution at time $t\in\R$. We assume that the initial probability  
measure
$\mu_0$ has zero mean, a translation-invariant covariance, and a  
finite mean
energy density. We also asume that $\mu_0$ satisfies a Rosenblatt- or
Ibragimov-Linnik-type mixing condition. The main result is the  
convergence of
$\mu_t$ to a Gaussian probability measure as $t\to\infty$ which gives  
a Central
Limit Theorem for the KGE. The proof for the case of constant  
coefficients is
based on an analysis of long time asymptotics of the solution in the  
Fourier
representation and Bernstein's `room-corridor' argument. The case of  
variable
coefficients is treated by using an `averaged' version of the  
scattering theory
for infinite energy solutions, based on Vainberg's results on local  
energy
decay.


http://front.math.ucdavis.edu/math-ph/0508042

---------------------------------------------------------------

3570. ON A TWO-TEMPERATURE PROBLEM FOR WAVE EQUATION

T.V. Dudnikova and  A.I. Komech and  H. Spohn

Consider the wave equation with constant or variable coefficients in $ 
\R^3$.
The initial datum is a random function with a finite mean density of  
energy
that also satisfies a Rosenblatt- or Ibragimov-Linnik-type mixing  
condition.
The random function converges to different space-homogeneous  
processes as
$x_3\to\pm\infty$, with the distributions $\mu_\pm$. We study the  
distribution
$\mu_t$ of the random solution at a time $t\in\R$. The main result is  
the
convergence of $\mu_t$ to a Gaussian translation-invariant measure as
$t\to\infty$ that means central limit theorem for the wave equation.  
The proof
is based on the Bernstein `room-corridor' argument. The application  
to the case
of the Gibbs measures $\mu_\pm=g_\pm$ with two different temperatures  
$T_{\pm}$
is given. Limiting mean energy current density formally is $-\infty\cdot
(0,0,T_+ -T_-)$ for the Gibbs measures, and it is finite and equals to
$-C(0,0,T_+ -T_-)$ with $C>0$ for the convolution with a nontrivial test
function.


http://front.math.ucdavis.edu/math-ph/0508044

---------------------------------------------------------------

3571. RAMDOM WALKS ON HYPERGROUP OF CIRCLES IN FINITE FIELDS

Le Anh Vinh

In this paper we study random walks on the hypergroup of circles in a  
finite
field of prime order p = 4l + 3. We investigating the behavior of  
random walks
on this hypergroup, the equilibrium distribution and the mixing  
times. We use
two different approaches - comparision of Dirichlet forms (geometric  
bound of
eigenvalues), and coupling methods, to show that the mixing time of  
random
walks on hypergroup of circles is only linear.


http://front.math.ucdavis.edu/math.CO/0508403

---------------------------------------------------------------

3572. MALLIAVIN CALCULUS FOR LIE GROUP-VALUED WIENER FUNCTIONS

Tai Melcher

Let G be a Lie group equipped with a set of left invariant vector  
fields.
These vector fields generate a function \xi on Wiener space into G  
via the
stochastic version of Cartan's rolling map. It is shown here that,  
for any
smooth function f with compact support, f(\xi) is Malliavin  
differentiable to
all orders and these derivatives belong to L^p(\mu) for all p>1,  
where \mu is
Wiener measure.


http://front.math.ucdavis.edu/math.PR/0508419

---------------------------------------------------------------

3573. ON A QUESTION OF CHUNG, DIACONIS, AND GRAHAM

Martin Hildebrand

Chung, Diaconis, and Graham considered random processes of the form
X_{n+1}=2X_n+b_n (mod p) where X_0=0, p is odd, and b_n for  
n=0,1,2,... are
i.i.d. random variables on {-1,0,1}. If Pr(b_n=-1)= Pr(b_n=1)=\beta and
Pr(b_n=0)=1-2\beta, they asked which value of \beta makes X_n get  
close to
uniformly distributed on the integers mod p the slowest. In this  
paper, we
extend the results of Chung, Diaconis, and Graham in the case p=2^t-1  
to show
that for 0<\beta<=1/2, there is no such value of \beta.


http://front.math.ucdavis.edu/math.PR/0508427

---------------------------------------------------------------

3574. LONG-RANGE PERCOLATION IN R^D

Bela Bollobas and  Svante Janson and Oliver Riordan

Let $X$ be either $Z^d$ or the points of a Poisson process in $R^d$ of
intensity 1. Given parameters $r$ and $p$, join each pair of points  
of $X$
within distance $r$ independently with probability $p$. This is the  
simplest
case of a `spread-out' percolation model studied by Penrose, who  
showed that,
as $r\to\infty$, the average degree of the corresponding random graph  
at the
percolation threshold tends to 1, i.e., the percolation threshold and  
the
threshold for criticality of the naturally associated branching process
approach one another. Here we show that this result follows  
immediately from of
a general result of the authors on inhomogeneous random graphs.


http://front.math.ucdavis.edu/math.PR/0508430

---------------------------------------------------------------

3575. HYPOELLIPTIC HEAT KERNEL INEQUALITIES ON LIE GROUPS

Tai Melcher

This paper discusses the existence of gradient estimates for second  
order
hypoelliptic heat kernels on manifolds. It is now standard that such
inequalities, in the elliptic case, are equivalent to a lower bound  
on the
Ricci tensor of the Riemannian metric. For hypoelliptic operators, the
associated ``Ricci curvature'' takes on the value -\infty at points of
degeneracy of the semi-Riemannian metric associated to the operator.  
For this
reason, the standard proofs for the elliptic theory fail in the  
hypoelliptic
setting.
   This paper presents recent results for hypoelliptic operators.  
Malliavin
calculus methods transfer the problem to one of determining certain  
infinite
dimensional estimates. Here, the underlying manifold is a Lie group,  
and the
hypoelliptic operators are invariant under left translation. In  
particular,
``L^p-type'' gradient estimates hold for p\in(1,\infty), and the p=2  
gradient
estimate implies a Poincar\'e estimate in this context.


http://front.math.ucdavis.edu/math.AP/0508420

---------------------------------------------------------------

3576. THE KLEE-MINTY RANDOM EDGE CHAIN MOVES WITH LINEAR SPEED

Jozsef Balogh and  Robin Pemantle

An infinite sequence of 0's and 1's evolves by flipping each~1 to a~0
exponentially at rate one. When a~1 flips, all bits to its right also  
flip.
Starting from any configuration with finitely many 1's to the left of  
the
origin, we show that the leftmost~1 moves right with linear speed.  
Upper and
lower bounds are given on the speed.


http://front.math.ucdavis.edu/math.PR/0506626

---------------------------------------------------------------

3577. FAST COMPUTATION OF THE ECONOMIC CAPITAL, THE VALUE AT RISK AND  
THE  GREEKS OF A LOAN PORTFOLIO IN THE GAUSSIAN FACTOR MODEL

P.Okunev

We propose a fast algorithm for computing the economic capital, Value  
at Risk
and Greeks in the Gaussian factor model. The algorithm proposed here  
is much
faster than brute force Monte Carlo simulations or Fourier transform  
based
methods \cite{MD}. While the algorithm of Hull-White \cite{HW} is  
comparably
fast, it assumes that all the loans in the portfolio have equal  
notionals and
recovery rates. This is a very restrictive assumption which is  
unrealistic for
many portfolios encountered in practice. Our algorithm makes no  
assumptions
about the homogeneity of the portfolio. Additionally, it is easier to  
implement
than the algorithm of Hull-White. We use the implicit function  
theorem to
derive analytic expressions for the Greeks.


http://front.math.ucdavis.edu/math.ST/0507082

---------------------------------------------------------------

3578. ON FILTERING OF MARKOV CHAINS IN STRONG NOISE

P.Chigansky

The filtering problem for a finite state Markov chain observed in  
white noise
is addressed in continuous time. The low signal to noise asymptotic  
is derived
for the performance indices of MAP and MMSE estimates of the signal.


http://front.math.ucdavis.edu/math.PR/0508446

---------------------------------------------------------------

3579. WEAK TYPE ESTIMATES ASSOCIATED TO BURKHOLDER'S MARTINGALE  
INEQUALITY

Javier Parcet

Given a probability space $(\Omega, \mathsf{A}, \mu)$, let $\mathsf{A} 
_1,
\mathsf{A}_2, ...$ be a filtration of $\sigma$-subalgebras of $\mathsf 
{A}$ and
let $\mathsf{E}_1, \mathsf{E}_2, ...$ denote the corresponding family of
conditional expectations. Given a martingale $f = (f_1, f_2, ...)$  
adapted to
this filtration and bounded in $L_p(\Omega)$ for some $2 \le p <  
\infty$,
Burkholder's inequality claims that $$\|f\|_{L_p(\Omega)} \sim_ 
{\mathrm{c}_p}
\Big\| \Big(\sum_{k=1}^\infty \mathsf{E}_{k-1}(|df_k|^2) \Big)^{1/2}
\Big\|_{L_{p}(\Omega)} + \Big(\sum_{k=1}^\infty \|df_k\|_p^p \Big)^{1/ 
p}.$$
Motivated by quantum probability, Junge and Xu recently extended this  
result to
the range $1 < p < 2$. In this paper we study Burkholder's inequality  
for
$p=1$, for which the techniques (as we shall explain) must be  
different. Quite
surprisingly, we obtain two non-equivalent estimates which play the  
role of the
weak type $(1,1)$ analog of Burkholder's inequality. As application,  
we obtain
new properties of Davis decomposition for martingales.


http://front.math.ucdavis.edu/math.PR/0508447

---------------------------------------------------------------

3580. UTILITY MAXIMIZATION IN INCOMPLETE MARKETS

Ying Hu and  Peter Imkeller and Matthias Muller

We consider the problem of utility maximization for small traders on
incomplete financial markets. As opposed to most of the papers  
dealing with
this subject, the investors' trading strategies we allow underly  
constraints
described by closed, but not necessarily convex, sets. The final wealths
obtained by trading under these constraints are identified as stochastic
processes which usually are supermartingales, and even martingales for
particular strategies. These strategies are seen to be optimal, and the
corresponding value functions determined simply by the initial values  
of the
supermartingales. We separately treat the cases of exponential, power  
and
logarithmic utility.


http://front.math.ucdavis.edu/math.PR/0508448

---------------------------------------------------------------

3581. EQUIVALENT AND ABSOLUTELY CONTINUOUS MEASURE CHANGES FOR JUMP- 
DIFFUSION  PROCESSES

Patrick Cheridito and  Damir Filipovic and Marc Yor

We provide explicit sufficient conditions for absolute continuity and
equivalence between the distributions of two jump-diffusion processes  
that can
explode and be killed by a potential.


http://front.math.ucdavis.edu/math.PR/0508450

---------------------------------------------------------------

3582. ON THE POWER OF TWO CHOICES: BALLS AND BINS IN CONTINUOUS TIME

Malwina J. Luczak and Colin McDiarmid

Suppose that there are n bins, and balls arrive in a Poisson process  
at rate
\lambda n, where \lambda >0 is a constant. Upon arrival, each ball  
chooses a
fixed number d of random bins, and is placed into one with least  
load. Balls
have independent exponential lifetimes with unit mean. We show that  
the system
converges rapidly to its equilibrium distribution; and when d\geq 2,  
there is
an integer-valued function m_d(n)=\ln \ln n/\ln d+O(1) such that, in the
equilibrium distribution, the maximum load of a bin is concentrated  
on the two
values m_d(n) and m_d(n)-1, with probability tending to 1, as n\to  
\infty. We
show also that the maximum load usually does not vary by more than a  
constant
amount from \ln \ln n/\ln d, even over quite long periods of time.


http://front.math.ucdavis.edu/math.PR/0508451

---------------------------------------------------------------

3583. HYPOELLIPTICITY IN INFINITE DIMENSIONS AND AN APPLICATION IN  
INTEREST  RATE THEORY

Fabrice Baudoin and Josef Teichmann

We apply methods from Malliavin calculus to prove an infinite- 
dimensional
version of Hormander's theorem for stochastic evolution equations in  
the spirit
of Da Prato-Zabczyk. This result is used to show that HJM-equations from
interest rate theory, which satisfy the Hormander condition, have the
conceptually undesirable feature that any selection of yields admits  
a density
as multi-dimensional random variable.


http://front.math.ucdavis.edu/math.PR/0508452

---------------------------------------------------------------

3584. THE COALESCENT EFFECTIVE SIZE OF AGE-STRUCTURED POPULATIONS

Serik Sagitov and Peter Jagers

We establish convergence to the Kingman coalescent for a class of
age-structured population models with time-constant population size.  
Time is
discrete with unit called a year. Offspring numbers in a year may  
depend on
mother's age.


http://front.math.ucdavis.edu/math.PR/0508454

---------------------------------------------------------------

3585. REPRESENTATION OF SOLUTIONS TO BSDES ASSOCIATED WITH A  
DEGENERATE FSDE

Jianfeng Zhang

In this paper we investigate a class of decoupled forward-backward SDEs,
where the volatility of the FSDE is degenerate and the terminal value  
of the
BSDE is a discontinuous function of the FSDE. Such an FBSDE is  
associated with
a degenerate parabolic PDE with discontinuous terminal condition. We  
first
establish a Feynman-Kac type representation formula for the spatial  
derivative
of the solution to the PDE. As a consequence, we show that there  
exists a
stopping time \tau such that the martingale integrand of the BSDE is  
continuous
before \tau and vanishes after \tau. However, it may blow up at \tau, as
illustrated by an example. Moreover, some estimates for the martingale
integrand before \tau are obtained. These results are potentially  
useful for
pricing and hedging discontinuous exotic options (e.g., digital  
options) when
the underlying asset's volatility is small, and they are also useful for
studying the rate of convergence of finite-difference approximations for
degenerate parabolic PDEs.


http://front.math.ucdavis.edu/math.PR/0508457

---------------------------------------------------------------

3586. THE SIZES OF THE PIONEERING, LOWEST CROSSING AND PIVOTAL SITES  
IN  CRITICAL PERCOLATION ON THE TRIANGULAR LATTICE

G. J. Morrow and Y. Zhang

Let L_n denote the lowest crossing of a square 2n\times2n box for  
critical
site percolation on the triangular lattice imbedded in Z^2. Denote  
also by F_n
the pioneering sites extending below this crossing, and Q_n the  
pivotal sites
on this crossing. Combining the recent results of Smirnov and Werner  
[Math.
Res. Lett. 8 (2001) 729-744] on asymptotic probabilities of multiple  
arm paths
in both the plane and half-plane, Kesten's [Comm. Math. Phys. 109 (1987)
109-156] method for showing that certain restricted multiple arm  
paths are
probabilistically equivalent to unrestricted ones, and our own second  
and
higher moment upper bounds, we obtain the following results. For each  
positive
integer \tau, as n\to\infty: 1. E(|L_n|^{\tau})=n^{4\tau/3+o(1)}. 2.
E(|F_n|^{\tau})=n^{7\tau/4+o(1)}. 3. E(|Q_n|^{\tau})=n^{3\tau/4+o 
(1)}. These
results extend to higher moments a discrete analogue of the recent  
results of
Lawler, Schramm and Werner [Math. Res. Lett. 8 (2001) 401-411] that the
frontier, pioneering points and cut points of planar Brownian motion  
have
Hausdorff dimensions, respectively, 4/3, 7/4 and 3/4.


http://front.math.ucdavis.edu/math.PR/0508459

---------------------------------------------------------------

3587. A LARGE DEVIATIONS APPROACH TO ASYMPTOTICALLY OPTIMAL CONTROL  
OF  CRISSCROSS NETWORK IN HEAVY TRAFFIC

Amarjit Budhiraja and Arka Prasanna Ghosh

In this work we study the problem of asymptotically optimal control of a
well-known multi-class queuing network, referred to as the ``crisscross
network,'' in heavy traffic. We consider exponential inter-arrival  
and service
times, linear holding cost and an infinite horizon discounted cost  
criterion.
In a suitable parameter regime, this problem has been studied in  
detail by
Martins, Shreve and Soner [SIAM J. Control Optim. 34 (1996)  
2133-2171] using
viscosity solution methods. In this work, using the pathwise solution  
of the
Brownian control problem, we present an elementary and transparent  
treatment of
the problem (with the identical parameter regime as in [SIAM J.  
Control Optim.
34 (1996) 2133-2171]) using large deviation ideas introduced in [Ann.  
Appl.
Probab. 10 (2000) 75-103, Ann. Appl. Probab. 11 (2001) 608-649]. We  
obtain an
asymptotically optimal scheduling policy which is of threshold type.  
The proof
is of independent interest since it is one of the few results which  
gives the
asymptotic optimality of a control policy for a network with a more than
one-dimensional workload process.


http://front.math.ucdavis.edu/math.PR/0508460

---------------------------------------------------------------

3588. THE PROBABILITY OF EXCEEDING A HIGH BOUNDARY ON A RANDOM TIME  
INTERVAL  FOR A HEAVY-TAILED RANDOM WALK

Serguei Foss and  Zbigniew Palmowski and Stan Zachary

We study the asymptotic probability that a random walk with heavy-tailed
increments crosses a high boundary on a random time interval. We use new
techniques to extend results of Asmussen [Ann. Appl. Probab. 8 (1998)  
354-374]
to completely general stopping times, uniformity of convergence over all
stopping times and a wide class of nonlinear boundaries. We also give  
some
examples and counterexamples.


http://front.math.ucdavis.edu/math.PR/0508461

---------------------------------------------------------------

3589. EQUILIBRIUM FOR FRAGMENTATION WITH IMMIGRATION

Benedicte Haas

This paper introduces stochastic processes that describe the  
evolution of
systems of particles in which particles immigrate according to a Poisson
measure and split according to a self-similar fragmentation. Criteria  
for
existence and absence of stationary distributions are established and
uniqueness is proved. Also, convergence rates to the stationary  
distribution
are given. Linear equations which are the deterministic counterparts of
fragmentation with immigration processes are next considered. As in the
stochastic case, existence and uniqueness of solutions, as well as  
existence
and uniqueness of stationary solutions, are investigated.


http://front.math.ucdavis.edu/math.PR/0508462

---------------------------------------------------------------

3590. CONVERGENCE OF RANDOM MEASURES IN GEOMETRIC PROBABILITY

Mathew D. Penrose

Given $n$ independent random marked $d$-vectors $X_i$ with a common  
density,
define the measure $\nu_n = \sum_i \xi_i $, where $\xi_i$ is a  
measure (not
necessarily a point measure) determined by the (suitably rescaled)  
set of
points near $X_i$. Technically, this means here that $\xi_i$  
stabilizes with a
suitable power-law decay of the tail of the radius of stabilization. For
bounded test functions $f$ on $R^d$, we give a law of large numbers  
and central
limit theorem for $\nu_n(f)$. The latter implies weak convergence of
$\nu_n(\cdot)$, suitably scaled and centred, to a Gaussian field  
acting on
bounded test functions. The general result is illustrated with  
applications
including the volume and surface measure of germ-grain models with  
unbounded
grain sizes.


http://front.math.ucdavis.edu/math.PR/0508464

---------------------------------------------------------------

3591. A SIMPLE SOLUTION TO THE K-CORE PROBLEM

Svante Janson and  Malwina Luczak

We study the k-core of a random (multi)graph on n vertices with a given
degree sequence. We let n tend to infinity. Then, under some regularity
conditions on the degree sequences, we give conditions on the  
asymptotic shape
of the degree sequence that imply that with high probability the k- 
core is
empty, and other conditions that imply that with high probability the  
k-core is
non-empty and the sizes of its vertex and edge sets satisfy a law of  
large
numbers; under suitable assumptions these are the only two  
possibilities. In
particular, we recover the result by Pittel, Spencer and Wormald on the
existence and size of a k-core in G(n,p) and G(n,m).
   Our method is based on the properties of empirical distributions of
independent random variables, and leads to simple proofs.


http://front.math.ucdavis.edu/math.CO/0508453

---------------------------------------------------------------

3592. CONCENTRATION OF HAAR MEASURES, WITH AN APPLICATION TO RANDOM  
MATRICES

Sourav Chatterjee

In this article, we present a general technique for analyzing the
concentration of Haar measures on compact groups using the properties of
certain kinds of random walks. As an application, we obtain a new  
kind of
measure concentration for random unitary matrices, which allows us to  
directly
establish the concentration of the empirical distribution of  
eigenvalues of a
class of random matrices. The end-result of this application is a  
quantitative
version of Voiculescu's celebrated connection between random matrices  
and free
probability.


http://front.math.ucdavis.edu/math.PR/0508518

---------------------------------------------------------------

3593. A GENERALIZATION OF THE LINDEBERG PRINCIPLE

Sourav Chatterjee

We present a generalization of Lindeberg's method of proving the central
limit theorem to encompass general smooth functions (instead of just  
sums) and
dependent random variables. The technique is then used to obtain an  
invariance
result for smooth functions of exchangeable random variables. As an
illustrative application of this theorem, we then establish  
``convergence to
Wigner's law'' for eigenspectra of matrices with exchangeable random  
entries.


http://front.math.ucdavis.edu/math.PR/0508519

---------------------------------------------------------------

3594. ON THE CASCADE ROLLBACK SYNCHRONIZATION

Anatoli Manita and Francois Simonot

We consider a cascade model of $N$ different processors performing a
distributed parallel simulation. The main goal of the study is to  
show that the
long-time dynamics of the system has a cluster behavior. To attack  
this problem
we combine two methods: stochastic comparison and Foster-Lyapunov  
functions.


http://front.math.ucdavis.edu/math.PR/0508533

---------------------------------------------------------------

3595. A BERNSTEIN-TYPE INEQUALITY FOR VECTOR FUNCTIONS ON FINITE  
MARKOV CHAINS

Vladislav Kargin

An analogue of the Bernstein inequality is derived for partial sums of a
vector-valued function on a finite reversible Markov chain. The  
inequality
gives an upper bound for the probability of a large deviation of the  
partial
sum. The bound depends on the chain's spectral gap, the dimension of  
the space
where the function takes values, and the upper bound on the size and the
variance of the function.


http://front.math.ucdavis.edu/math.PR/0508538

---------------------------------------------------------------

3596. ON THE CONVERGENCE TO A STATISTICAL EQUILIBRIUM IN THE CRYSTAL  
COUPLED  TO A SCALAR FIELD

T.V. Dudnikova and  A.I. Komech

We consider the dynamics of a field coupled to a harmonic crystal  
with $n$
components in dimension $d$, $d,n\ge 1$. The crystal and the dynamics  
are
translation-invariant with respect to the subgroup $\Z^d$ of $\R^d$. The
initial data is a random function with a finite mean density of  
energy which
also satisfies a Rosenblatt- or Ibragimov-Linnik-type mixing condition.
Moreover, initial correlation functions are translation-invariant  
with respect
to the discrete subgroup $\Z^d$. We study the distribution $\mu_t$ of  
the
solution at time $t\in\R$. The main result is the convergence of $ 
\mu_t$ to a
Gaussian measure as $t\to\infty$, where $\mu_\infty$ is translation- 
invariant
with respect to the subgroup $\Z^d$.


http://front.math.ucdavis.edu/math-ph/0508053

---------------------------------------------------------------

3597. CONNECTION BETWEEN DERIVING BRIDGES AND RADIAL PARTS FROM   
MULTIDIMENSIONAL ORNSTEIN-UHLENBECK PROCESSES

Matyas Barczy and Gyula Pap

First we give a construction of bridges derived from a general Markov  
process
using only its transition densities. We give sufficient conditions  
for their
existence and uniqueness (in law). Then we prove that the law of the  
radial
part of the bridge with endpoints zero derived from a special  
multidimensional
Ornstein-Uhlenbeck process equals the law of the bridge with  
endpoints zero
derived from the radial part of the same Ornstein-Uhlenbeck process.  
We also
construct bridges derived from general multidimensional Ornstein- 
Uhlenbeck
processes.


http://front.math.ucdavis.edu/math.PR/0508542

---------------------------------------------------------------

3598. VALLEYS AND THE MAXIMUM LOCAL TIME FOR RANDOM WALK IN RANDOM  
ENVIRONMENT

Amir Dembo and  Nina Gantert and  Yuval Peres and  Zhan Shi

Let $\xi(n, x)$ be the local time at $x$ for a recurrent one-dimensional
random walk in random environment after $n$ steps, and consider the  
maximum
$\xi^*(n) = \max_x \xi(n,x)$. It is known that $\limsup \xi^*(n)/n$ is a
positive constant a.s. We prove that $\liminf_n (\log\log\log n)\xi^* 
(n)/n$ is
a positive constant a.s.; this answers a question of P. R\'ev\'esz  
(1990). The
proof is based on an analysis of the {\em valleys /} in the environment,
defined as the potential wells of record depth. In particular, we  
show that
almost surely, at any time $n$ large enough, the random walker has  
spent almost
all of its lifetime in the two deepest valleys of the environment it has
encountered. We also prove a uniform exponential tail bound for the  
ratio of
the expected total occupation time of a valley and the expected local  
time at
its bottom.


http://front.math.ucdavis.edu/math.PR/0508579

---------------------------------------------------------------

3599. RANDOM-TURN HEX AND OTHER SELECTION GAMES

Yuval Peres and  Oded Schramm and  Scott Sheffield and  David B. Wilson

The game of Hex has two players who take turns placing stones of  
their colors
on the hexagons of a rhombus-shaped hexagonal grid. Black wins by  
completing a
crossing between two opposite edges, while White wins by completing a  
crossing
between the other pair of opposite edges. Although ordinary Hex is  
famously
difficult to analyze, random-turn Hex--in which players toss a coin  
before each
turn to decide who gets to place the next stone--has a simple optimal  
strategy.
It belongs to a general class of random-turn games--called selection  
games--in
which the expected payoff when both players play the random-turn game  
optimally
is the same as when both players play randomly. We also describe the  
optimal
strategy and study the expected length of the game under optimal play  
for
random-turn Hex and several other selection games.


http://front.math.ucdavis.edu/math.PR/0508580

---------------------------------------------------------------

3600. NUMERICAL SOLUTIONS TO INTEGRODIFFERENTIAL EQUATIONS WHICH  
INTERPOLATE  HEAT AND WAVE EQUATIONS

Piotr Rozmej and Anna Karczewska

In the paper we study some numerical solutions to Volterra equations  
which
interpolate heat and wave equations. We present a scheme for  
construction of
approximate numerical solutions for one and two spatial dimensions. Some
solutions to the stochastic version of such equations (for one spatial
dimension) are presented as well.


http://front.math.ucdavis.edu/math.NA/0508564

---------------------------------------------------------------

3601. DISTRIBUTED ALGORITHMS IN AN ERGODIC MARKOVIAN ENVIRONMENT

Francis Comets (PMA) and  Francois Delarue (PMA) and  Rene Schott  
(IEC and  LORIA)

We provide a probabilistic analysis of the banker algorithm when  
transition
probabilities may depend on time and space. The transition probabilities
evolve, as time goes by, along the trajectory of an ergodic Markovian
environment, whereas the spatial parameter just acts on long runs.  
Our model
appears as a new (small) step towards more general time and space  
dependent
protocols. Our analysis relies on well-known results in stochastic
homogenization theory and investigates the asymptotic behaviour of  
the rescaled
algorithm as the total amount of resource available for allocation  
tends to the
infinity. In the two dimensional setting, we manage to exhibit three  
different
possible regimes for the deadlock time of the limit system.


http://front.math.ucdavis.edu/math.PR/0507115

---------------------------------------------------------------

3602. ON MULTIDIMENSIONAL BRANCHING RANDOM WALKS IN RANDOM ENVIRONMENT

Francis Comets (PMA) and  Serguei Popov (IME)

We study branching random walks in random i.i.d. environment in $ 
\Z^d, d \geq
1$. For this model, the population size cannot decrease, and a natural
definition of recurrence is introduced. We prove a dichotomy for
recurrence/transience, depending only on the support of the  
environmental law.
We give sufficient conditions for recurrence and for transience. In the
recurrent case, we study the asymptotics of the tail of the  
distribution of the
hitting times and prove a shape theorem for the set of lattice sites  
which are
visited up to a large time.


http://front.math.ucdavis.edu/math.PR/0507126

---------------------------------------------------------------

3603. COMPETITION BETWEEN GROWTHS GOVERNED BY BERNOULLI PERCOLATION

Olivier Garet (MAPMO) and  R\'{e}gine Marchand (IEC)

We study a competition model on $\mathbb{Z}^d$ where the two  
infections are
driven by supercritical Bernoulli percolations with distinct  
parameters $p$ and
$q$. We prove that, for any $q$, there exist at most countably many  
values of
$p<\min(q, \overrightarrow{p\_c})$ such that coexistence can occur.


http://front.math.ucdavis.edu/math.PR/0507133

---------------------------------------------------------------

3604. POLYMER PINNING IN A RANDOM MEDIUM AS INFLUENCE PERCOLATION

Vincent Beffara (UMPA-ENSL) and  Vladas Sidoravicius (BR-IMPA) and   
Herbert  Spohn (D-MUTU-ZM), Eulalia Vares (BR-CBPF)

In this article we discuss a set of geometric ideas which shed some  
light on
the question of directed polymer pinning in the presence of bulk  
disorder.
Differing from standard methods and techniques, we transform the  
problem to a
particular dependent percolative system and relate the pinning  
transition to a
percolation transition.


http://front.math.ucdavis.edu/math.PR/0507142

---------------------------------------------------------------

3605. LINEAR STOCHATIC DIFFERENTIAL-ALGEBRAIC EQUATIONS WITH  
CONSTANT  COEFFICIENTS

Aureli Alabert and  Marco Ferrante

We consider linear stochastic differential-algebraic equations with  
constant
coefficients and additive white noise. Due to the nature of this  
class of
equations, the solution must be defined as a generalised process (in  
the sense
of Dawson and Fernique). We provide sufficient conditions for the law  
of the
variables of the solution process to be absolutely continuous with  
respect to
Lebesgue measure.


http://front.math.ucdavis.edu/math.PR/0507159

---------------------------------------------------------------

3606. LIKELIHOOD INFERENCE FOR INCOMPLETELY OBSERVED STOCHASTIC  
PROCESSES:  IGNORABILITY CONDITIONS

Daniel Commenges and  Anne Gegout-Petit

We define a general coarsening model for stochastic processes. We  
decribe
incomplete data by means of sigma-fields and we give conditions of  
ignorability
for likelihood inference.


http://front.math.ucdavis.edu/math.ST/0507151

---------------------------------------------------------------

3607. DETERMINISTIC EQUIVALENTS FOR CERTAIN FUNCTIONALS OF LARGE  
RANDOM  MATRICES

W. Hachem and  P. Loubaton and  J. Najim

Consider a $N\times n$ random matrix $ Y_n$ where the entries are  
independent
but not identically distributed (matrices with a variance profile)  
Consider now
a deterministic $N\times n$ matrix $A_n$ whose columns and rows are  
uniformly
bounded for the Euclidean norm.
   Let $\Sigma_n=Y_n+A_n$. We prove in this article that there exists a
deterministic equivalent to the empirical Stieltjes transform of the
distribution of the eigenvalues of $\Sigma_n \Sigma_n^T$ which is  
itself the
Stieltjes transform of a probability measure.
   This work is motivated by the context of performance evaluation of  
Multiple
Inputs / Multiple Output (MIMO) wireless digital communication  
channels. As an
application, we derive a deterministic equivalent to the mutual  
information of
a wireless channel.


http://front.math.ucdavis.edu/math.PR/0507172

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3608. A RENEWAL THEORY APPROACH TO PERIODIC COPOLYMERS WITH ADSORPTION

Francesco Caravenna and  Giambattista Giacomin and Lorenzo Zambotti

We consider a general model of an heterogeneous polymer chain  
fluctuating in
the proximity of an interface between two selective solvents. The  
heterogeneous
character of the model comes from the fact that monomer units  
interact with the
solvents and with the interface according to some charges that they  
carry. The
charges repeat themselves along the chain in a periodic fashion. The  
main
question on this model is whether the polymer remains tightly close  
to the
interface, a phenomenon called localization, or there is a marked  
preference
for one of the two solvents yielding thus a delocalization phenomenon.
   We propose an approach to this model, based on renewal theory,  
that yields
sharp estimates on the partition function of the model in all the  
regimes
(localized, delocalized and critical). This in turn allows to get a very
precise description of the polymer measure, both in a local sense
(thermodynamic limit) and in a global sense (scaling limits). A key  
point, but
also a byproduct, of our analysis is the closeness of the polymer  
measure to
suitable Markov Renewal Processes.


http://front.math.ucdavis.edu/math.PR/0507178

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3609. LEVY PROCESSES: HITTING TIME, OVERSHOOT AND UNDERSHOOT II -  
ASYMPTOTIC  BEHAVIOUR

Bernard Roynette and  Pierre Vallois and  Agnes Volpi

Let (X_t, t>=0) be a Levy process started at 0, with Levy measure nu  
and T_x
the first hitting time of level x>0: T_x:=inf{t>=0; X_t>x}. Let $F 
(theta, mu,
rho,.) be the joint Laplace transform of (T_x, K_x, L_x): F 
(theta,mu,rho,x)
:=E(e^(-theta T_x - mu K_x \rho L_x) 1_(T_x<+infinity)), where  
theta>=0, mu>=0,
rho>=0, x>=0, K_x:=X_(T_x)-x and L_x:=x-X_(T_(x^-)). If we assume  
that nu has
finite exponential moments we exhibit an asymptotic expansion for
F(theta,mu,rho,x), as x -> +infinity. A limit theorem involving a  
normalization
of the triplet (T_x,K_x,L_x) as x -> +infinity, may be deduced. At  
last, if
nu_(|_R_+) has finite moment of fixed order, we prove that the ruin  
probability
P(T_x<+infinity) has at most a polynomial decay.


http://front.math.ucdavis.edu/math.PR/0507193

---------------------------------------------------------------

3610. COMPLETENESS WITH RESPECT TO THE PROBABILISTIC POMPEIU- 
HAUSDORFF METRIC

Stefan Cobza\c{s}

The aim of the present paper is to prove that the family of all closed
nonempty subsets of a complete probabilistic metric space $L$ is  
complete with
respect to the probabilistic Pompeiu-Hausdorff metric $H$. The same  
is true for
the families of all closed bounded, respectively compact, nonempty  
subsets of
$L$. If $L$ is a complete random normed space in the sense of \v{S} 
erstnev,
then the family of all nonempty closed convex subsets of $L$ is also  
complete
with respect to $H$.


http://front.math.ucdavis.edu/math.PR/0507207

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3611. PERCOLATION THEORY

Vincent Beffara (UMPA-ENSL) and  Vladas Sidoravicius (IMPA)

This is a survey article to be part of the Encyclopedia of Mathematical
Physics, to be published by Elsevier in the beginning of 2006.


http://front.math.ucdavis.edu/math.PR/0507220

---------------------------------------------------------------

3612. THE RANDOM AVERAGE PROCESS AND RANDOM WALK IN A SPACE-TIME  
RANDOM  ENVIRONMENT IN ONE DIMENSION

Marton Balazs and  Firas Rassoul-Agha and Timo Seppalainen

We study space-time fluctuations around a characteristic line for a
one-dimensional interacting system known as the random average  
process. The
state of this system is a real-valued function on the integers. New  
values of
the function are created by averaging previous values with random  
weights. The
fluctuations analyzed occur on the scale n^{1/4} where n is the ratio of
macroscopic and microscopic scales in the system. The limits of the
fluctuations are described by a family of Gaussian processes. In  
cases of known
product-form equilibria, this limit is a two-parameter process whose  
time
marginals are fractional Brownian motions with Hurst parameter 1/4.  
Along the
way we study the limits of quenched mean processes for a random walk  
in a
space-time random environment. These limits also happen at scale n^ 
{1/4} and
are described by certain Gaussian processes that we identify. In  
particular,
when we look at a backward quenched mean process, the limit process  
is the
solution of a stochastic heat equation.


http://front.math.ucdavis.edu/math.PR/0507226

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3613. A NEW EFFICIENT ALGORITHM FOR CONSTRUCTION OF LLS MODELS

Mikhail Kovtun and  Igor Akushevich and  Kenneth G. Manton and  H.  
Dennis Tolley

We present a new efficient algortithm for construction of linear latent
structure (LLS) models. This algorithm reduces a problem of  
estimation of model
parameters to a sequence of problems of linear algebra, which assures  
a low
computational complexity and ability to handle on desktop computers  
data that
involve up to thousands of variables.


http://front.math.ucdavis.edu/math.PR/0507021

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3614. BROWNIAN SHEET AND REFLECTIONLESS POTENTIALS

Setsuo Taniguchi

The bijectivity of the mapping, which is represented as expectation,  
from a
family of Gaussian measures parametrized by linear combinations of Dirac
measures to the space of classical reflectionless potentials is  
shown. It is
also shown that the bijectivity extends to the space of generalized
reflectionless potentials, which was used by V. Marchenko to study  
the Cauchy
problem for the KdV equation. In the extension, the stochastic  
calculus based
on the Brownian sheet plays a key role.


http://front.math.ucdavis.edu/math.PR/0507229

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3615. ANALYTICITY OF ENTROPY RATE IN FAMILIES OF HIDDEN MARKOV CHAINS

Guangyue Han and  Brian Marcus

We prove that under a mild positivity assumption the entropy rate of  
a hidden
Markov chain varies analytically as a function of the underlying  
Markov chain
parameters. We give examples to show how this can fail in some cases.  
And we
study two natural special classes of hidden Markov chains in more  
detail:
binary hidden Markov chains with an unambiguous symbol and binary  
Markov chains
corrupted by binary symmetric noise. Finally, we show that under the  
positivity
assumption the hidden Markov chain {\em itself} varies analytically,  
in a
strong sense, as a function of the underlying Markov chain parameters.


http://front.math.ucdavis.edu/math.PR/0507235

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3616. LIKELY PATH TO EXTINCTION FOR SIMPLE BRANCHING MODEL (LARGE  
DEVIATIONS  APPROACH)

F. Klebaner and  R. Liptser

We give an explicit formula for the most likely path to extinction  
for the
Galton-Watson processes with large initial population. We establish  
this result
with the help of the large deviation principle (LDP) which also  
recovers the
asymptotics of extinction probability.
   Due to the nonnegativity of the Galton-Watson processes, the proof  
of LDP
verification at the point of extinction uses a nonstandard argument of
independent interest.


http://front.math.ucdavis.edu/math.PR/0507257

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3617. CRAMER'S THEOREM FOR NONNEGATIVE SUMMANDS

F. Klebaner and  R. Liptser

We clarify the boundary effect in Cramer's theorem on the Large  
Deviations
Principle (LDP) for normed sums of non-negative i.i.d. random  
variables $
S_n=\frac{1}{n}\sum_{i=1}^n\xi_i $. We show that the LDP holds true  
with the
rate function possibly infinite at the boundary point $x=0$.
   We also consider a continuous time version of Cramer's theorem with
nonnegative summands $ S_t=\frac{1}{t}\sum_{i:\tau_i\le t}\xi_i, t \to 
\infty, $
where $(\tau_i,\xi_i)_{i\ge 1}$ is a sequence of random variables  
such that
$tS_t$ is a random process with independent increments.


http://front.math.ucdavis.edu/math.PR/0507258

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3618. STATIONARITY OF SWITCHING VAR AND OTHER RELATED MODELS

Gopal K. Basak and Zhan-Qian Lu

Switching ARMA models greatly enhance the standard linear models to the
extent that different ARMA model is allowed in a different regime,  
and the
regime switching is typically assumed a Markov chain on the finite  
states of
potential regimes. Although statistical issues have been the subject  
of many
recent papers, there is few systematic study of the probabilistic  
aspects of
this new class of nonlinear models. This paper discusses some basic  
issues
concerning this class of models including strict stationarity,  
influence of
initial conditions, and second-order property by studying SVAR  
models. A number
of examples are given to illustrate the theory and the variety of  
applications.
Extensions to other models such as mean-shifting, and inhomogeneous  
transition
probabilities are discussed.


http://front.math.ucdavis.edu/math.ST/0507267

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3619. THE FERMAT CUBIC, ELLIPTIC FUNCTIONS, CONTINUED FRACTIONS, AND  
A  COMBINATORIAL EXCURSION

Eric van Fossen Conrad and Philippe Flajolet

Elliptic functions considered by Dixon in the nineteenth century and  
related
to Fermat's cubic, $x^3+y^3=1$, lead to a new set of continued fraction
expansions with sextic numerators and cubic denominators. The  
functions and the
fractions are pregnant with interesting combinatorics, including a  
special
P\'olya urn, a continuous-time branching process of the Yule type, as  
well as
permutations satisfying various constraints that involve either  
parity of
levels of elements or a repetitive pattern of order three. The  
combinatorial
models are related to but different from models of elliptic functions  
earlier
introduced by Viennot, Flajolet, Dumont, and Fran{\c{c}}on.


http://front.math.ucdavis.edu/math.CO/0507268

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3620. EARTHQUAKE RECURRENCE AS A RECORD BREAKING PROCESS

Joern Davidsen and  Peter Grassberger and Maya Paczuski

We extend the notion of waiting times for a point process to  
recurrent events
in space-time. Earthquake $B$ is a recurrence of a previous one, $A$,  
if no
intervening earthquake happens after $A$ and before $B$ in the  
spatial disc
centered on $A$ with radius $\bar{AB}$. The cascade of recurrent  
events, where
each later recurrence to an event is closer in space than all  
previous ones,
forms a sequence of records. Representing each record by a directed link
between nodes defines a network of earthquakes. For Southern  
California, this
network exhibits robust scaling laws. The rupture length emerges as a
fundamental scale for distance between recurrent events. Also, the  
distribution
of relative separations for the next record in space (time) $\sim
r^{-\delta_r}$ ($\sim t^{-\delta_t}$), with $\delta_r \approx  
\delta_t \approx
0.6$. While the in-degree distribution agrees with a random network, the
out-degree distribution shows large deviations from Poisson statistics.
Comparison with randomized data and a theory of records for  
independent events
occurring on a fractal shows that these statistics capture non- 
trivial features
of the complex spatiotemporal organization of seismicity.


http://front.math.ucdavis.edu/physics/0507082

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3621. LINEAR LATENT STRUCTURE ANALYSIS: MIXTURE DISTRIBUTION MODELS  
WITH  LINEAR CONSTRAINTS

Mikhail Kovtun and  Igor Akushevich and  Kenneth G. Manton and  H.  
Dennis Tolley

A new method for analyzing high-dimensional categorical data, Linear  
Latent
Structure (LLS) analysis, is presented. LLS models belong to the  
family of
latent structure models, which are mixture distribution models  
constrained to
satisfy the local independence assumption. LLS analysis explicitly  
considers a
family of mixed distributions as a linear space and LLS models are  
obtained by
imposing linear constraints on the mixing distribution. LLS models are
identifiable under modest conditions and are consistently estimable. A
remarkable feature of LLS analysis is the existence of a high- 
performance
numerical algorithm, which reduces parameter estimation to a sequence  
of linear
algebra problems. Preliminary simulation experiments with a prototype  
of the
algorithm demonstrated a good quality of restoration of model  
parameters.


http://front.math.ucdavis.edu/math.PR/0507025

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3622. EULER INTEGRALS FOR COMMUTING SLES

Julien Dubedat

Schramm-Loewner Evolutions (SLEs) have proved an efficient way to  
describe a
single continuous random conformally invariant interface in a simply  
connected
planar domain; the admissible probability distributions are  
parameterized by a
single positive parameter $\kappa$. As shown in \cite{D6}, the  
coexistence of
$n$ interfaces in such a domain implies algebraic ("commutation")  
conditions.
In the most interesting situations, the admissible laws on systems of  
$n$
interfaces are parameterized by $\kappa$ and the solution of  
particular (finite
rank) holonomic systems. The study of solutions of differential  
systems, in
particular their global behaviour, often involves the use of integral
representations. In the present article, we provide Euler integral
representations for solutions of holonomic systems arising from SLE
commutation. Applications to critical percolation (general crossing  
formulae),
loop-erased random walks (direct derivation of Fomin's formulae in  
the scaling
limit), and uniform spanning trees are discussed. The connection with  
conformal
restriction and Poissonized non-intersection for chordal SLEs is also  
studied.


http://front.math.ucdavis.edu/math.PR/0507276

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3623. BRYC'S RANDOM FIELDS: THE EXISTENCE AND DISTRIBUTIONS ANALYSIS

Wojciech Matysiak and  Pawe{\l} J. Szab{\l}owski

We examine problem of existence of stationary random fields with linear
regressions and quadratic conditional variances, introduced by Bryc in
"Stationary random fields with linear regressions" (Annals of  
Probability 29,
No. 1, 504-519). Distributions of the fields are identified and  
almost complete
description of the possible sets of parameters defining the first two
conditional moments is given. This note almost solves Bryc's problem  
concerning
fields undetermined by moments - the only remaining set of parameters  
for which
the existence of Bryc's fields is unclear has Lebesgue measure zero.


http://front.math.ucdavis.edu/math.PR/0507296

---------------------------------------------------------------

3624. Q-WIENER AND RELATED PROCESSES. A BRYC PROCESSES CONTINUOUS  
TIME  GENERALIZATION

Pawe{\l} J. Szab{\l}owski

We define two Markov processes. The finite dimensional distributions  
of the
first one (say $\mathbf{X=}(X_{t})_{t\geq0})$ depend on one parameter
$q\in(-1,1>$ and of the second one (say $\mathbf{Y=}(Y_{t})_{t\in 
\mathbb{R}})$
on two parameters $(q,\alpha) \in(-1,1>\times(0,\infty).$ The first one
resembles Wiener process in the sense that for $q=1$ it is Wiener  
process but
also that for $q<1$ and $\forall n\geq1$ $t^{n/2}H_{n}(X_{t}/\sqrt{t}| 
q) ,$
where $(H_{n})_{n\geq0}$ are so called $q-$Hermite polynomials, are
martingales. It does not have however independent increments. The  
second one
resemble Orstein-Ulehnbeck processes. For $q=1$ it is a classical OU  
process.
For $q<1$ it is stationary with correlation function equal to $\exp
(-\alpha|t-s|).$When defining these processes and proving their  
existence we
use properties of discrete time Bryc processes and solve the problem  
of their
existence for $q>1.$ On the way we deny Wesolowski's martingale
characterization of Wiener process.


http://front.math.ucdavis.edu/math.PR/0507303

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3625. THE MIXING TIME OF THE THORP SHUFFLE

Ben Morris

The Thorp shuffle is defined as follows. Cut the deck into two equal  
piles.
Drop the first card from the left pile or the right pile according to  
the
outcome of a fair coin flip; then drop from the other pile. Continue  
this way
until both piles are empty. We show that the mixing time for the  
Thorp shuffle
with $2^d$ cards is polynomial in $d$.


http://front.math.ucdavis.edu/math.PR/0507307

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3626. TAIL BOUNDS FOR THE STABLE MARRIAGE OF POISSON AND LEBESGUE

Christopher Hoffman and  Alexander E. Holroyd and Yuval Peres

Let \Xi be a discrete set in R^d. Call the elements of \Xi centers. The
well-known Voronoi tessellation partitions R^d into polyhedral  
regions (of
varying volumes) by allocating each site of R^d to the closest  
center. Here we
study allocations of R^d to \Xi in which each center attempts to  
claim a region
of equal volume \alpha.
   We focus on the case where \Xi arises from a Poisson process of unit
intensity. It was proved in math.PR/0505668 that there is a unique  
allocation
which is stable in the sense of the Gale-Shapley marriage problem. We  
study the
distance X from a typical site to its allocated center in the stable
allocation.
   The model exhibits a phase transition in the appetite \alpha. In  
the critical
case \alpha=1 we prove a power law upper bound on X in dimension d=1.  
It is an
open problem to prove any upper bound in d\geq 2. (Power law lower  
bounds were
proved in math.PR/0505668 for all d). In the non-critical cases  
\alpha<1 and
\alpha>1 we prove exponential upper bounds on X.


http://front.math.ucdavis.edu/math.PR/0507324

---------------------------------------------------------------

3627. NON-MARKOV RANDOM FIELDS WITH LINEAR REGRESSIONS - A TOEPLITZ  
OPERATORS  APPROACH

Wojciech Matysiak and  Pawe{\l} J. Szab{\l}owski

The aim of the paper is to analyze square integrable random sequences
$\mathbf{X}=(X_{k})_{k\in\mathbb{Z}}$ satisfying condition \[
\wwo{X_k}{...,X_{k-2},X_{k-1},X_{k+1},X_{k+2},...}=\sum_{j=1}^n b_j
(X_{k-j}+X_{k+j}) \] with $b_{j}\in\mathbb{R}$ and
$n\in\nat\cup\left\{+\infty\right\}$. The question of existence of such
sequences for all $n\in\mathbb{N}$ including $n=+\infty$ is examined  
and some
conditions guaranteeing existence are provided. In order to give these
conditions we analyze general problem of existence of processes  
defined by
regression coefficients. The problem is closely related to one  
considered by
Kingman and Williams.
   One of the results presented in the paper is that one sided  
regressions of
$\mathbf{X}$ are also linear: \[
\mathbb{E}(X_{k}|...,X_{k-2},X_{k-1})=\sum_{j=1}^{n}\beta_{j}X_{k -j} 
% \] for
some $\beta_{j}\in\mathbb{R}$ and with the same $n$ as before.


http://front.math.ucdavis.edu/math.PR/0507332

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3628. RECTANGULAR RANDOM MATRICES, RELATED CONVOLUTION

Florent Benaych-Georges (DMA)

We characterize asymptotic collective behaviour of rectangular random
matrices, the sizes of which tend to infinity at different rates:  
when embedded
in a space of larger square matrices, independent rectangular random  
matrices
are asymtotically free with amalgamation over a subalgebra. Therefore  
we can
define a "rectangular free convolution", linearized by cumulants and  
by an
analytic integral transform, called the "rectangular R-transform".


http://front.math.ucdavis.edu/math.PR/0507336

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3629. LIMIT SHAPES OF MULTIPLICATIVE MEASURES ASSOCIATED WITH   
COAGULATION-FRAGMENTATION PROCESSES AND RANDOM COMBINATORIAL STRUCTURES

Michael Erlihson and Boris Granovsly

We find limit shapes for a family of multiplicative measures on the  
set of
partitions, induced by exponential generating functions with expansive
parameters, $a_k\sim k^{p-1}, k\to\infty, p>0$. The measures  
considered are
associated with reversible coagulation-fragmentation processes and  
certain
combinatorial structures. We prove the functional central limit  
theorem for the
fluctuations of a scaled random partition around its limit shape. We  
also
demonstrate that when the component size passes beyond the threshold  
value, the
independence of numbers of components transforms into their conditional
independence. Among other things, the paper discusses, in a general  
setting,
the interplay between limit shapes, threshold and gelation.


http://front.math.ucdavis.edu/math.PR/0507343

---------------------------------------------------------------

3630. CONDITIONAL ASSOCIATION AND SPIN SYSTEMS

Thomas M. Liggett

A 1977 theorem of T. Harris states that an attractive spin system  
preserves
the class of associated probability measures. We study analogues of  
this result
for measures that satisfy various conditional positive correlations  
properties.
In particular, we show that a spin system preserves measures  
satisfying the FKG
lattice condition (essentially) if and only if distinct spins flip
independently. The downward FKG property, which has been useful  
recently in the
study of the contact process, lies between the properties of lattice  
FKG and
association. We prove that this property is preserved by a spin  
system if the
death rates are constant and the birth rates are additive (e.g., the  
contact
process), and prove a partial converse to this statement. Finally, we  
introduce
a new property, which we call downward conditional association, which  
lies
between the FKG lattice condition and downward FKG, and find essentially
necessary and sufficient conditions for this property to be preserved  
by a spin
system. This suggests that the latter property may be more natural  
than the
downward FKG property.


http://front.math.ucdavis.edu/math.PR/0507392

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3631. SOME RESULTS CONCERNING MAXIMUM RENYI ENTROPY DISTRIBUTIONS

Oliver Johnson and Christophe Vignat

We consider the Student-t and Student-r distributions, which maximise  
Renyi
entropy under a covariance condition. We show that they have
information-theoretic properties which mirror those of the Gaussian
distributions, which maximise Shannon entropy under the same  
condition. We
introduce a convolution which preserves the Renyi maximising family,  
and show
that the Renyi maximisers are the case of equality in a version of  
the Entropy
Power Inequality. Further, we show that the Renyi maximisers satisfy  
a version
of the heat equation, motivating the definition of a generalized Fisher
information.


http://front.math.ucdavis.edu/math.PR/0507400

---------------------------------------------------------------

3632. RECURRENCE FOR PERSISTENT RANDOM WALKS IN TWO DIMENSIONS

Marco Lenci

We discuss the question of recurrence for persistent, or Newtonian,  
random
walks in Z^2, i.e., random walks whose transition probabilities  
depend both on
the walker's position and incoming direction. We use results by Toth and
Schmidt-Conze to prove recurrence for a large class of such processes,
including all "invertible" walks in elliptic random environments.  
Furthermore,
rewriting our Newtonian walks as ordinary random walks in a suitable  
graph, we
gain a better idea of the geometric features of the problem, and  
obtain further
examples of recurrence.


http://front.math.ucdavis.edu/math.PR/0507411

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3633. DONSKER THEOREMS FOR DIFFUSIONS: NECESSARY AND SUFFICIENT  
CONDITIONS

Aad van der Vaart and Harry van Zanten

We consider the empirical process G_t of a one-dimensional diffusion  
with
finite speed measure, indexed by a collection of functions F. By the  
central
limit theorem for diffusions, the finite-dimensional distributions of  
G_t
converge weakly to those of a zero-mean Gaussian random process G. We  
prove
that the weak convergence G_t\Rightarrow G takes place in \ell^ 
{\infty}(F) if
and only if the limit G exists as a tight, Borel measurable map. The  
proof
relies on majorizing measure techniques for continuous martingales.
Applications include the weak convergence of the local time density  
estimator
and the empirical distribution function on the full state space.


http://front.math.ucdavis.edu/math.PR/0507412

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3634. THE MULTIFRACTAL SPECTRUM OF BROWNIAN INTERSECTION LOCAL TIMES

Achim Klenke and Peter Morters

Let \ell be the projected intersection local time of two independent  
Brownian
paths in R^d for d=2,3. We determine the lower tail of the random  
variable
\ell(U), where U is the unit ball. The answer is given in terms of  
intersection
exponents, which are explicitly known in the case of planar Brownian  
motion. We
use this result to obtain the multifractal spectrum, or spectrum of thin
points, for the intersection local times.


http://front.math.ucdavis.edu/math.PR/0507437

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3635. VALIDITY OF THE EXPECTED EULER CHARACTERISTIC HEURISTIC

Jonathan Taylor and  Akimichi Takemura and Robert J. Adler

We study the accuracy of the expected Euler characteristic  
approximation to
the distribution of the maximum of a smooth, centered, unit variance  
Gaussian
process f. Using a point process representation of the error, valid for
arbitrary smooth processes, we show that the error is in general  
exponentially
smaller than any of the terms in the approximation. We also give a  
lower bound
on this exponential rate of decay in terms of the maximal variance of  
a family
of Gaussian processes f^x, derived from the original process f.


http://front.math.ucdavis.edu/math.PR/0507442

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3636. LEVY PROCESSES: HITTING TIME, OVERSHOOT AND UNDERSHOOT - PART  
I:  FUNCTIONAL EQUATIONS

Bernard Roynette and  Pierre Vallois and  Agnes Volpi

Let (X_t, t >=0) be a Levy process started at 0, with Levy measure  
nu, and
T_x the first hitting time of level x>0: T_x := inf{t>=0; X_t>x}. Let
F(theta,mu,rho,.) be the joint Laplace transform of (T_x, K_x, L_x):
F(theta,mu,rho,x) := E (e^{-theta T_x - mu K_x - rho L_x} 1_{T_x< 
+infinity}),
where theta>=0, mu>=0, rho>=0, x>0, K_x := X_{T_x} - x and L_x := x -
X_{T_{x^-}}. If nu(R) < + \infinity and integral_1^{+\infty} e^{sy}  
nu (dy) <
+infinity for some s>0, then we prove that F(theta,mu,rho,.) is the  
unique
solution of an integral equation and has a subexponential decay at  
infinity
when theta>0 or theta=0 and E(X_1)<0. If nu is not necessarily a  
finite measure
but verifies integral_{-infinity}^{-1} e^{-sy} nu (dy) < +infinity  
for any s>0,
then the x-Laplace transform of F(theta,mu,rho,.) satisfies some kind of
integral equation. This allows us to prove that F(theta,mu,rho,.) is  
a solution
to a second integral equation.


http://front.math.ucdavis.edu/math.PR/0507034

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3637. CORNER PERCOLATION ON Z^2 AND THE SQUARE ROOT OF 17

Gabor Pete

We consider a dependent bond percolation model on Z^2, introduced by  
Balint
Toth, in which every edge is present with probability 1/2, and each  
vertex has
exactly two incident edges, perpendicular to each other. We prove  
that all
components are finite cycles almost surely, but the expected diameter  
of the
cycle containing the origin is infinite. A more detailed analysis  
leads to the
derivation of the following critical exponents: the tail probability
\Pr(diameter of the cycle of the origin > n) \approx n^{-\gamma}, and  
the
expectation \E(length of a cycle conditioned on having diameter n)  
\approx
n^\delta. We show that \gamma=(5-\sqrt{17})/4=0.219... and
\delta=(\sqrt{17}+1)/4=1.28... The relation \gamma+\delta=3/2  
corresponds to
the fact that the scaling limit of the natural height function in the  
model is
the Additive Brownian Motion, whose level sets have Hausdorff  
dimension 3/2.


http://front.math.ucdavis.edu/math.PR/0507457

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3638. BARYCENTERS OF MEASURES TRANSPORTED BY STOCHASTIC FLOWS

Marc Arnaudon and Xue-Mei Li

We investigate the evolution of barycenters of masses transported by
stochastic flows. The state spaces under consideration are smooth affine
manifolds with certain convexity structure. Under suitable conditions  
on the
flow and on the initial measure, the barycenter {Z_t} is shown to be a
semimartingale and is described by a stochastic differential  
equation. For the
hyperbolic space the barycenter of two independent Brownian particles  
is a
martingale and its conditional law converges to that of a Brownian  
motion on
the limiting geodesic. On the other hand for a large family of discrete
measures on suitable Cartan-Hadamard manifolds, the barycenter of the  
measure
carried by an unstable Brownian flow converges to the Busemann  
barycenter of
the limiting measure.


http://front.math.ucdavis.edu/math.PR/0507460

---------------------------------------------------------------

3639. STOCHASTIC EQUIVARIANT COHOMOLOGIES AND CYCLIC COHOMOLOGY

Remi Leandre

We give two stochastic diffeologies on the free loop space which  
allow us to
define stochastic equivariant cohomology theories in the Chen-Souriau  
sense and
to establish a link with cyclic cohomology. With the second one, we can
establish a stochastic fixed point theorem.


http://front.math.ucdavis.edu/math.PR/0507461

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3640. SOME RESULTS ON TWO-SIDED LIL BEHAVIOR

Uwe Einmahl and Deli Li

Let {X,X_n;n\geq 1} be a sequence of i.i.d. mean-zero random  
variables, and
let S_n=\sum_{i=1}^nX_i,n\geq 1. We establish necessary and sufficient
conditions for having with probability 1, 0<lim sup_{n\to
\infty}|S_n|/\sqrtnh(n)<\infty, where h is from a suitable subclass  
of the
positive, nondecreasing slowly varying functions. Specializing our  
result to
h(n)=(\log \log n)^p, where p>1 and to h(n)=(\log n)^r, r>0, we obtain
analogues of the Hartman-Wintner LIL in the infinite variance case.  
Our proof
is based on a general result dealing with LIL behavior of the  
normalized sums
{S_n/c_n;n\ge 1}, where c_n is a sufficiently regular normalizing  
sequence.


http://front.math.ucdavis.edu/math.PR/0507462

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3641. RANDOM WALK ATTRACTED BY PERCOLATION CLUSTERS

Serguei Popov and  Marina Vachkovskaia

Starting with a percolation model in $\Z^d$ in the subcritical  
regime, we
consider a random walk described as follows: the probability of  
transition from
$x$ to $y$ is proportional to some function $f$ of the size of the  
cluster of
$y$. This function is supposed to be increasing, so that the random  
walk is
attracted by bigger clusters. For $f(t)=e^{\beta t}$ we prove that  
there is a
phase transition in $\beta$, i.e., the random walk is subdiffusive  
for large
$\beta$ and is diffusive for small $\beta$.


http://front.math.ucdavis.edu/math.PR/0507054

---------------------------------------------------------------

3642. LIMIT THEOREMS FOR THE TYPICAL POISSON-VORONOI CELL AND THE  
CROFTON CELL  WITH A LARGE INRADIUS

Pierre Calka and Tomasz Schreiber

In this paper, we are interested in the behavior of the typical
Poisson-Voronoi cell in the plane when the radius of the largest disk  
centered
at the nucleus and contained in the cell goes to infinity. We prove a  
law of
large numbers for its number of vertices and the area of the cell  
outside the
disk. Moreover, for the latter, we establish a central limit theorem  
as well as
moderate deviation type results. The proofs deeply rely on precise  
connections
between Poisson-Voronoi tessellations, convex hulls of Poisson  
samples and
germ-grain models in the unit ball. Besides, we derive analogous  
facts for the
Crofton cell of a stationary Poisson line process in the plane.


http://front.math.ucdavis.edu/math.PR/0507463

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3643. STATISTICAL DUALITY OF THE LAPLACE DISTRIBUTION

E.A. Barkova and  S.I. Bityukov and  V.A. Taperechkina

The statistical duality of distributions is a powerful tool for  
statistical
inferences. In the paper the statistical duality of Laplace  
distribution is
discussed. As shown the confidence density of the parameter of this
distribution is uniquely determined.


http://front.math.ucdavis.edu/math.ST/0507452

---------------------------------------------------------------

3644. ESTIMATES FOR MOMENTS OF RANDOM MATRICES WITH GAUSSIAN ELEMENTS

O. Khorunzhiy

We describe an elementary method to get non-asymptotic estimates for the
moments of hermitian random matrices whose elements are gaussian  
independent
random variables. As the basic example, we consider the GUE matrices.  
Immediate
applications include GOE and gaussian skew-symmetric hermitian matrices.


http://front.math.ucdavis.edu/math-ph/0507060

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3645. DISTANCES BETWEEN THE WINNING NUMBERS IN LOTTERY

Konstantinos Drakakis

We prove an interesting fact about Lottery: the winning 6 numbers  
(out of 49)
in the game of the Lottery contain two consecutive numbers with a  
surprisingly
high probability (almost 50%).


http://front.math.ucdavis.edu/math.CO/0507469

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3646. A GENERAL LOWER BOUND FOR MIXING OF SINGLE-SITE DYNAMICS ON GRAPHS

Thomas P. Hayes and Alistair Sinclair

We prove that any Markov chain that performs local, reversible  
updates on
randomly chosen vertices of a bounded-degree graph necessarily has  
mixing time
at least $\Omega(n\log n)$, where $n$ is the number of vertices. Our  
bound
applies to the so-called ``Glauber dynamics'' that has been used  
extensively in
algorithms for the Ising model, independent sets, graph colorings and  
other
structures in computer science and statistical physics, and  
demonstrates that
many of these algorithms are optimal up to constant factors within  
their class.
Previously no super-linear lower bound for this class of algorithms  
was known.
Though widely conjectured, such a bound had been proved previously  
only in very
restricted circumstances, such as for the empty graph and the path.  
We also
show that the assumption of bounded degree is necessary by giving a  
family of
dynamics on graphs of unbounded degree with mixing time $O(n)$.


http://front.math.ucdavis.edu/math.PR/0507517


From pas at www.economia.unimi.it  Mon Nov  7 09:23:59 2005
From: pas at www.economia.unimi.it (pas@www.economia.unimi.it)
Date: Mon Nov  7 09:25:07 2005
Subject: [Pas] Probability Abstracts 89
Message-ID: <C2191F7A-8CBD-4E53-BCFD-14E38F411D9C@unimi.it>

					November 7, 2005

							Letter 89

Probability Abstract Service

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3647. MULTIPLE DECORRELATION AND RATE OF CONVERGENCE IN  
MULTIDIMENSIONAL LIMIT  THEOREMS FOR THE PROKHOROV METRIC

Francoise Pene

The motivation of this work is the study of the error term
e_t^{\epsilon}(x,\omega) in the averaging method for differential  
equations
perturbed by a dynamical system. Results of convergence in  
distribution for
(\frac{e_t^{\epsilon}(x,\cdot)}{\sqrt\epsilon})_{\epsilon>0} have been
established in Khas'minskii [Theory Probab. Appl. 11 (1966) 211-228],  
Kifer
[Ergodic Theory Dynamical Systems 15 (1995) 1143-1172] and P\`ene [ESAIM
Probab. Statist. 6 (2002) 33-88]. We are interested here in the  
question of the
rate of convergence in distribution of the family of random variables
(\frac{e_t^{\epsilon}(x,\cdot)}{\sqrt\epsilon})_{\epsilon>0} when  
\epsilon goes
to 0 (t>0 and x\inR^d being fixed). We will make an assumption of  
multiple
decorrelation property (satisfied in several situations). We start by
establishing a simpler result: the rate of convergence in the central  
limit
theorem for regular multidimensional functions. In this context, we  
prove a
result of convergence in distribution with rate of convergence in
O(n^{-1/2+\alpha}) for all \alpha>0 (for the Prokhorov metric). This  
result can
be seen as an extension of the main result of P\`ene [Comm. Math.  
Phys. 225
(2002) 91-119] to the case of d-dimensional functions. In a second  
time, we use
the same method to establish a result of convergence in distribution for
(\frac{e_t^{\epsilon}(x,\cdot)}{\sqrt\epsilon})_{\epsilon>0} with  
rate of
convergence in O(\epsilon^{1/2-\alpha}) (for the Prokhorov metric).


http://front.math.ucdavis.edu/math.PR/0509008

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3648. CONTINUUM TREE LIMIT FOR THE RANGE OF RANDOM WALKS ON REGULAR  
TREES

Thomas Duquesne (Paris 11)

Let $b$ be an integer greater than 1 and let $W^{\ee}=(W^{\ee}_n; n 
\geq 0)$
be a random walk on the $b$-ary rooted tree $\U_b$, starting at the  
root, going
up (resp. down) with probability $1/2+\epsilon$ (resp. $1/2 -\epsilon$),
$\epsilon \in (0, 1/2)$, and choosing direction $i\in \{1, ..., b\}$  
when going
up with probability $a_i$. Here $\aa =(a_1, ..., a_b)$ stands for some
non-degenerated fixed set of weights. We consider the range $\{W^{\ee} 
_n ;
n\geq 0 \}$ that is a subtree of $\U_b $. It corresponds to a unique  
random
rooted ordered tree that we denote by $\tau_{\epsilon}$. We rescale  
the edges
of $\tau_{\epsilon}$ by a factor $\ee $ and we let $\ee$ go to 0: we  
prove that
correlations due to frequent backtracking of the random walk only  
give rise to
a deterministic phenomenon taken into account by a positive factor $ 
\gamma
(\aa)$. More precisely, we prove that $\tau_{\epsilon}$ converges to a
continuum random tree encoded by two independent Brownian motions  
with drift
conditioned to stay positive and scaled in time by $\gamma (\aa)$. We  
actually
state the result in the more general case of a random walk on a tree  
with an
infinite number of branches at each node ($b=\infty$) and for a  
general set of
weights $\aa =(a_n, n\geq 0)$.


http://front.math.ucdavis.edu/math.PR/0509524

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3649. AN EXPLICIT SKOROKHOD EMBEDDING FOR FUNCTIONALS OF MARKOVIAN  
EXCURSIONS

Jan Obloj (PMA and  Mimuw)

We develop an explicit non-randomized solution to the Skorokhod  
embedding
problem in an abstract setup of signed functionals of Markovian  
excursions. Our
setting allows to solve the Skorokhod embedding problem, in  
particular, for
diffusions and their (signed, scaled) age processes, for Azema's  
martingale,
for spectrally one-sided Levy processes and their reflected versions,  
for
Bessel processes of dimension smaller than 2, and for their age  
processes, as
well as for the age process of excursions of Cox-Ingersoll-Ross  
processes. This
work is a continuation and an important generalization of Obloj and  
Yor (SPA
110) [35]. Our methodology, following [35], is based on excursion  
theory and
the solution to the Skorokhod embedding problem is described in terms  
of the
Ito measure of the functional. We also derive an embedding for positive
functionals and we correct a mistake in the formula in [35] for  
measures with
atoms.


http://front.math.ucdavis.edu/math.PR/0509553

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3650. DIFFUSIONS IN RANDOM ENVIRONMENT AND BALLISTIC BEHAVIOR

Tom Schmitz

This article is accepted for publication in the "Annals I.H.P. Prob. &
Stat.". We investigate the ballistic behavior of diffusions in random
environment. We introduce conditions in the spirit of (T) and (T') of  
the
discrete setting, cf. Sznitman \cite{szn01}, \cite{szn02}, that imply  
in higher
dimensions a strong law of large numbers with non-vanishing limiting  
velocity
(which we refer to as 'ballistic behavior') and a functional central  
limit
theorem with non-degenerate covariance matrix. As an application of our
results, we consider the class of diffusions where the diffusion  
matrix is the
identity, and give a concrete criterion on the drift term under which  
the
diffusion in random environment exhibits ballistic behavior. This  
criterion
provides new examples of ballistic diffusions in random environment.


http://front.math.ucdavis.edu/math.PR/0509554

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3651. RANDOM TREES, LEVY PROCESSES AND SPATIAL BRANCHING PROCESSES

Thomas Duquesne (Paris 11) and  Jean-Francois Le Gall (Ecole Normale   
Superieure de Paris and Paris 6)

We investigate the genealogical structure of general critical or  
subcritical
continuous-state branching processes. Analogously to the coding of a  
discrete
tree by its contour function, this genealogical structure is coded by a
real-valued stochastic process called the height process, which is  
itself
constructed as a local time functional of a Levy process with no  
negative
jumps. We present a detailed study of the height process and of an  
associated
measure-valued process called the exploration process, which plays a  
key role
in most applications. Under suitable assumptions, we prove that  
whenever a
sequence of rescaled Galton-Watson processes converges in  
distribution, their
genealogies also converge to the continuous branching structure coded  
by the
appropriate height process. We apply this invariance principle to  
various
asymptotics for Galton-Watson trees. We then use the duality  
properties of the
exploration process to compute explicitly the distribution of the  
reduced tree
associated with Poissonnian marks in the height process, and the
finite-dimensional marginals of the so-called stable continuous tree.  
This last
calculation generalizes to the stable case a result of Aldous for the  
Brownian
continuum random tree. Finally, we combine the genealogical structure  
with an
independent spatial motion to develop a new approach to  
superprocesses with a
general branching mechanism. In this setting, we derive certain explicit
distributions, such as the law of the spatial reduced tree in a domain,
consisting of the collection of all historical paths that hit the  
boundary.


http://front.math.ucdavis.edu/math.PR/0509558

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3652. DECOMPOSITIONS OF STOCHASTIC PROCESSES BASED ON IRREDUCTIBLE  
GROUP  REPRESENTATIONS

Giovanni Peccati (LSTA) and  Jean-Renaud Pycke (DP)

Let G be a topological compact group acting on some space Y. We study a
decomposition of Y-indexed stochastic processes, based on the  
orthogonality
relations between the characters of the irreducible representations  
of G. In
the particular case of a Gaussian process with a G-invariant law, such a
decomposition gives a very general explanation of a classic identity  
in law -
between quadratic functionals of a Brownian bridge - due to Watson  
(1961).
Several relations with Karhunen-Lo\`{e}ve expansions are discussed,  
and some
applications and extensions are given - in particular related to  
Gaussian
processes indexed by a torus.


http://front.math.ucdavis.edu/math.PR/0509569

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3653. OPTIMAL PHYLOGENETIC RECONSTRUCTION

Constantinos Daskalakis and Elchanan Mossel and Sebastien Roch

It is well known that in order to reconstruct a tree on $n$ leaves,  
sequences
of length $\Omega(\log n)$ are needed. It was conjectured by M. Steel  
that for
the CFN evolutionary model, if the mutation probability on all edges  
of the
tree is less than $p^{\ast} = (\sqrt{2}-1)/2^{3/2}$ than the tree can be
recovered from sequences of length $O(\log n)$. This was proven by  
the second
author in the special case where the tree is ``balanced''. The second  
author
also proved that if all edges have mutation probability larger than  
$p^{\ast}$
then the length needed is $n^{\Omega(1)}$. This ``phase-transition''  
in the
number of samples needed is closely related to the phase transition  
for the
reconstruction problem (or extremality of free measure) studied  
extensively in
statistical physics and probability.
   Here we complete the proof of Steel's conjecture and give a  
reconstruction
algorithm using optimal (up to a multiplicative constant) sequence  
length. Our
results further extend to obtain optimal reconstruction algorithm for  
the
Jukes-Cantor model with short edges. All reconstruction algorithms  
run in time
polynomial in the sequence length.
   The algorithm and the proofs are based on a novel combination of
combinatorial, metric and probabilistic arguments.


http://front.math.ucdavis.edu/math.PR/0509575

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3654. SLOW EMERGENCE OF COOPERATION FOR WIN-STAY LOSE-SHIFT ON TREES

Elchanan Mossel and Sebastien Roch

We consider a group of agents on a graph who repeatedly play the  
prisoner's
dilemma game against their neighbors. The players adapt their actions  
to the
past behavior of their opponents by applying the win-stay lose-shift  
strategy.
On a finite connected graph, it is easy to see that the system learns to
cooperate by converging to the all-cooperate state in a finite time.  
We analyze
the rate of convergence in terms of the size and structure of the  
graph. [Dyer
et al., 2002] showed that the system converges rapidly on the cycle,  
but that
it takes a time exponential in the size of the graph to converge to  
cooperation
on the complete graph. We show that the emergence of cooperation is
exponentially slow in some expander graphs. More surprisingly, we  
show that it
is also exponentially slow in bounded-degree trees, where many other  
dynamics
are known to converge rapidly.


http://front.math.ucdavis.edu/math.PR/0509576

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3655. LIMIT THEOREMS FOR NUMBER OF DIFFUSION PROCESSES WHICH DID NOT  
ABSORB  BY BOUNDARIES

Aniello Fedullo and Vitalii A. Gasanenko

We have random number of independent diffusion processes with  
absorption on
boundaries in some region at initial time $t=0$. The initial numbers and
positions of processes in region is defined by Poisson random  
measure. It is
required to estimate of number of the unabsorbed processes for the  
fixed time
\~$\tau>0$. The Poisson random measure depends on $\tau$ and $\tau\to 
\infty$.


http://front.math.ucdavis.edu/math.PR/0509585

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3656. LIMIT RARING PROCESES WITH APLLICATION

Vitalii A. Gasanenko

This paper deals with study of the sufficient condition of approximation
raring process with mixing by renewall process. We consider use the  
proved
results to practice problem too


http://front.math.ucdavis.edu/math.PR/0509586

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3657. THE PRINCIPLE OF A SINGLE BIG JUMP: DISCRETE AND CONTINUOUS  
TIME  MODULATED RANDOM WALKS WITH HEAVY-TAILED INCREMENTS

Serguei Foss and  Takis Konstantopoulos and Stan Zachary

We consider a modulated process S which, conditional on a background  
process
X, has independent increments. Assuming that S drifts to -infinity  
and that its
increments (jumps) are heavy-tailed (in a sense made precise in the  
paper), we
exhibit natural conditions under which the asymptotics of the tail  
distribution
of the overall maximum of S can be computed. We present results in  
discrete and
in continuous time. In particular, in the absence of modulation, the  
process S
in continuous time reduces to a Levy process with heavy-tailed Levy  
measure. A
central point of the paper is that we make full use of the so-called
``principle of a single big jump'' in order to obtain both upper and  
lower
bounds. Thus, the proofs are entirely probabilistic. The paper is  
motivated by
queueing and Levy stochastic networks.


http://front.math.ucdavis.edu/math.PR/0509605

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3658. FURTHER EXAMPLES OF EXPLICIT KREIN REPRESENTATIONS OF CERTAIN   
SUBORDINATORS

Catherine Donati-Martin (PMA) and  Marc Yor (PMA)

In a previous paper, we have shown that the gamma subordinators may be
represented as inverse local times of certain diffusions. In the  
present paper,
we give such representations for other subordinators whose L\'evy  
densities are
of the form $ \frac{\mathcal{C}}{(\sinh(y))^\gamma}$, $0 < \gamma < 2 
$, and the
more general family obtained from those by exponential tilting.


http://front.math.ucdavis.edu/math.PR/0509041

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3659. THE SPECTRUM OF THE AVERAGING OPERATOR ON A NETWORK (METRIC GRAPH)

Donald I. Cartwright and Wolfgang Woess

A network is a countable, connected graph X viewed as a one-complex,  
where
each edge [x,y]=[y,x] (x,y in X^0, the vertex set) is a copy of the unit
interval within the graph's one-skeleton X^1 and is assigned a positive
conductance c(xy). A reference "Lebesgue" measure on X^1 is built up  
by using
Lebesgue measure with total mass c(xy) on each edge [x,y]. There are  
three
natural operators on X : the transition operator P acting on  
functions on X^0
(the reversible Markov chain associated with the conductances), the  
averaging
operator A over spheres of radius 1 on X^1, and the Laplace operator  
on X^1
(with Kirchhoff conditions weighted by c(.) at the vertices). The  
relation
between the l^2-spectrum of P and the H^2-spectrum of the Laplacian was
described by Cattaneo (Mh. Math. 124, 1997). In this paper we  
describe the
relation between the l^2-spectrum of P and the L^2-spectrum of A.


http://front.math.ucdavis.edu/math.FA/0509595

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3660. ERGODIC BEHAVIOUR OF LOCALLY REGULATED BRANCHING POPULATIONS

Martin Hutzenthaler and  Anton Wakolbinger

For a class of processes modeling the evolution of a spatially  
structured
population with migration and a logistic local regulation of the  
reproduction
dynamics we show convergence towards an upper invariant measure from  
a suitable
class of initial distributions. It follows from recent work of A.  
Etheridge
that this upper invariant measure is non-trivial for sufficiently large
super-criticality in the reproduction. For sufficiently small super- 
criticality
we prove local extinction by comparison with a mean field model. This  
latter
result extends also to more general local reproduction regulations.


http://front.math.ucdavis.edu/math.PR/0509612

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3661. NONLINEAR STOCHASTIC MODELS OF 1/F NOISE AND POWER-LAW  
DISTRIBUTIONS

Bronislovas Kaulakys and  Julius Ruseckas and  Vygintas Gontis and  
Miglius  Alaburda

Starting from the developed generalized point process model of $1/f$  
noise
(B. Kaulakys et al, Phys. Rev. E 71 (2005) 051105; cond-mat/0504025)  
we derive
the nonlinear stochastic differential equations for the signal  
exhibiting
1/f^{\beta}$ noise and $1/x^{\lambda}$ distribution density of the  
signal
intensity with different values of $\beta$ and $\lambda$. The  
processes with
$1/f^{\beta}$ are demonstrated by the numerical solution of the derived
equations with the appropriate restriction of the diffusion of the  
signal in
some finite interval. The proposed consideration may be used for  
modeling and
analysis of stochastic processes in different systems with the power-law
distributions, long-range memory or with the elements of self- 
organization.


http://front.math.ucdavis.edu/cond-mat/0509626

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3662. LIMIT LAWS FOR DISTORTED RETURN TIME PROCESSES FOR INFINITE  
MEASURE  PRESERVING TRANSFORMATIONS

Marc Kesseb\"ohmer and Mehdi Slassi

We consider conservative ergodic measure preserving transformations on
infinite measure spaces and investigate the asymptotic behaviour of  
distorted
return time processes with respect to sets satisfying a type of  
Darling-Kac
condition. As applications we derive asymptotic laws for the  
normalized Kac
process and the normalized spent time Kac process. We introduce the  
notion of
uniformly returning sets, for which we prove that if the wandering  
rate is
slowly varying then the normalized spent time Kac process converges  
strongly
distributional to a random variable uniformly distributed on the unit  
interval.


http://front.math.ucdavis.edu/math.DS/0509609

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3663. PDE'S FOR THE GAUSSIAN ENSEMBLE WITH EXTERNAL SOURCE AND THE  
PEARCEY  DISTRIBUTION

Mark Adler & Pierre van Moerbeke

The present paper studies a Gaussian Hermitian random matrix ensemble  
with
external source, given by a fixed diagonal matrix with two  
eigenvalues a and
-a. As a first result, the probability that the eigenvalues of the  
ensemble
belong to a set satisfies a fourth order PDE with quartic non- 
linearity; the
variables being the eigenvalue a and the boundary points of the set.  
This
equation enables one to find a PDE for the Pearcey distribution. The  
latter
describes the statistics of the eigenvalues near the closure of a  
gap; i.e.,
when the support of the equilibrium measure for large size random  
matrices has
a gap, which can be made to close. Precisely, the Gaussian Hermitian  
random
matrix ensemble with external source has this feature. In this work,  
we show
the Pearcey distribution satisfies a a fourth order PDE with cubic
non-linearity. The PDE for the finite problem is found by by showing  
that an
appropriate integrable deformation of the random matrix ensemble with  
external
source satisfies the three-component KP equation and Virasoro  
constraints.


http://front.math.ucdavis.edu/math.PR/0509047

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3664. CENTRAL LIMIT THEOREM FOR STATIONARY LINEAR PROCESSES

Magda Peligrad and Sergey Utev

We establish the central limit theorem for linear processes with  
dependent
innovations including martingales and mixingale type of assumptions  
as defined
in McLeisch (1977) and motivated by Gordin (1969). In doing so we shall
preserve the generality of the coefficients, including the long range
dependence case, and we shall express the variance of partial sums in  
a form
easy to apply. Ergodicity is not required.


http://front.math.ucdavis.edu/math.PR/0509682

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3665. THE HAUSDORFF MEASURE OF STABLE TREES

Thomas Duquesne (Universite Paris 11); Jean-Francois Le Gall (Ecole   
Normale superieure et Universite Paris 6)

We study fine properties of the so-called stable trees, which are the  
scaling
limits of critical Galton-Watson trees conditioned to be large. In  
particular
we derive the exact Hausdorff measure function for Aldous' continuum  
random
tree and for its level sets. It follows that both the uniform measure  
on the
tree and the local time measure on a level set coincide with certain  
Hausdorff
measures. Slightly less precise results are obtained for the  
Hausdorff measure
of general stable trees.


http://front.math.ucdavis.edu/math.PR/0509690

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3666. LOCALIZATION AND DELOCALIZATION OF RANDOM INTERFACES

Yvan Velenik (LMRS)

The study of effective interface models has been quite active  
recently, with
a particular emphasis on the effect of various external potentials  
(wall,
pinning potential, ...) leading to localization/delocalization  
transitions. I
review some of the results that have been obtained. In particular, I  
discuss
pinning by a local potential, entropic repulsion and the (pre)wetting
transition, both for models with continuous and discrete heights.  
This text is
based on lecture notes for a mini-course given during the workshop  
"Topics in
Random Interfaces and Directed Polymers" held in Leipzig, September  
12-17 2005.


http://front.math.ucdavis.edu/math.PR/0509695

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3667. ON SOME RECENT ASPECTS OF STOCHASTIC CONTROL THEORY AND THEIR   
APPLICATIONS

Huyen Pham (PMA)

This paper is a survey on some recent aspects and developments in  
stochastic
control theory. We discuss the two main historical approaches, Bellman's
optimality principle and Pontryagin's maximum principle, and their  
modern
exposition with viscosity solutions and backward stochastic differential
equations. Some original proofs are presented in a unifying context  
including
degenerate singular controlControlled diffusions, dynamic  
programming, maximum
principle, viscosity solutions, backward stochastic differential  
equations,
finance. problems. We emphasize key results on characterization of  
optimal
control for diffusion processes, with a view towards applications. Some
examples in finance are detailed with their explicit solutions. We  
also discuss
numerical issues and open questions.


http://front.math.ucdavis.edu/math.PR/0509711

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3668. RECURSIVE COMPUTATION OF THE INVARIANT MEASURE OF A STOCHASTIC   
DIFFERENTIAL EQUATION DRIVEN BY A L\'{E}VY PROCESS

Fabien Panloup (PMA)

We investigate some recursive procedures based on an exact or  
``approximate''
Euler scheme with decreasing step in vue to computation of invariant  
measures
of solutions to S.D.E. driven by a L\'{e}vy process. Our results are  
valid for
a large class of S.D.E. that can be governed by L\'{e}vy processes  
with few
moments or can have a weakly mean-reverting drift, and permit to find  
again the
a.s. C.L.T for stable processes.


http://front.math.ucdavis.edu/math.PR/0509712

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3669. STOCHASTIC EMBEDDING OF DYNAMICAL SYSTEMS

Jacky Cresson (LM-Besan\c{c}on) and  S\'{e}bastien Darses  (LM-Besan\c 
{c}on)

Most physical systems are modelled by an ordinary or a partial  
differential
equation, like the n-body problem in celestial mechanics. In some  
cases, for
example when studying the long term behaviour of the solar system or for
complex systems, there exist elements which can influence the  
dynamics of the
system which are not well modelled or even known. One way to take these
problems into account consists of looking at the dynamics of the  
system on a
larger class of objects, that are eventually stochastic. In this  
paper, we
develop a theory for the stochastic embedding of ordinary differential
equations. We apply this method to Lagrangian systems. In this  
particular case,
we extend many results of classical mechanics namely, the least action
principle, the Euler-Lagrange equations, and Noether's theorem. We  
also obtain
a Hamiltonian formulation for our stochastic Lagrangian systems. Many
applications are discussed at the end of the paper.


http://front.math.ucdavis.edu/math.PR/0509713

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3670. DYSON'S BROWNIAN MOTIONS, INTERTWINING AND INTERLACING

Jon Warren

A family of reflected Brownian motions is used to construct Dyson's  
process
of non-colliding Brownian motions. A number of explicit formulae are  
given,
including one for the distribution of a family of coalescing Brownian  
motions.


http://front.math.ucdavis.edu/math.PR/0509720

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3671. SELF-INTERSECTION TIMES FOR RANDOM WALK, AND RANDOM WALK IN  
RANDOM  SCENERY IN DIMENSIONS D>4

Amine Asselah Fabienne Castell

We consider Random Walk in Random Scenery , denoted $X_n$, where the  
random
walk is symmetric on $Z^d$, with $d>4$, and the random field is made  
up of
i.i.d random variables with a stretched exponential tail decay, with  
exponent
$\alpha$ with $1<\alpha$. We present asymptotics for the probability,  
over both
randomness, that $\{X_n>n^{\beta}\}$ for $1/2<\beta<1$. To obtain such
asymptotics, we establish large deviations estimates for the the
self-intersection local times process.


http://front.math.ucdavis.edu/math.PR/0509721

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3672. NON-NEGATIVITY PRESERVING NUMERICAL ALGORITHMS FOR STOCHASTIC   
DIFFERENTIAL EQUATIONS

Esteban Moro and  Henri Schurz

Construction of splitting-step methods and properties of related
non-negativity and boundary preserving numerical algorithms for solving
stochastic differential equations (SDEs) of Ito-type are discussed.  
We present
convergence proofs for a newly designed splitting-step algorithm and  
simulation
studies for numerous numerical examples ranging from stochastic dynamics
occurring in asset pricing theory in mathematical finance (SDEs of  
CIR and CEV
models) to measure-valued diffusion and superBrownian motion (SPDEs)  
as met in
biology and physics.


http://front.math.ucdavis.edu/math.NA/0509724

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3673. LIMIT THEOREMS ON LARGE DEVIATIONS FOR SEMIMARTINGALES

Robert Sh. Liptser and Anatolii A. Pukhalskii

We consider a sequence $X^n=(X^n_t)_{t\ge 0},n\ge 1$ of  
semimartingales. Each
$X^n$ is a weak solution to an It\^o equation with respect to a  
Wiener process
and a Poissonian martingale measure and is in general non-Markovian  
process.
For this sequence, we prove the large deviation principle in the  
Skorokhod
space $D=D_{[0,\infty)}$. We use a new approach based on of exponential
tightness. This allows us to establish the large deviation principle  
under
weaker assumptions than before.


http://front.math.ucdavis.edu/math.PR/0510028

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3674. LARGE DEVIATIONS FOR TWO SCALED DIFFUSIONS

R. Liptser

We formulate large deviations principle (LDP) for diffusion pair
$(X^\epsilon,\xi^\epsilon)=(X_t^\epsilon,\xi_t^\epsilon)$, where first
component has a small diffusion parameter while the second is ergodic  
Markovian
process with fast time. More exactly, the LDP is established for
$(X^\epsilon,\nu^\epsilon)$ with $\nu^\epsilon(dt,dz)$ being an  
occupation type
measure corresponding to $\xi_t^\epsilon$. In some sense we obtain a
combination of Freidlin-Wentzell's and Donsker-Varadhan's results.  
Our approach
relies the concept of the exponential tightness and Puhalskii's theorem.


http://front.math.ucdavis.edu/math.PR/0510029

---------------------------------------------------------------

3675. SOLVABLE MODELS OF NEIGHBOR-DEPENDENT NUCLEOTIDE SUBSTITUTION  
PROCESSES

Jean B\'erard and  Jean-Baptiste Gou\'er\'e and  Didier Piau

We prove that a wide class of models of Markov neighbor-dependent
substitution processes on the integer line is solvable. This class  
contains
some models of nucleotide substitutions recently introduced and studied
empirically by molecular biologists. We show that the frequency of every
polynucleotide at equilibrium solves an explicit finite-sized linear  
system.
Finally, the dynamics of the process and the distribution at equilibrium
exhibit some stringent, unexpected, independence properties. For  
example,
nucleotide sites at distance at least three evolve independently, and  
the
sites, if encoded as purines and pyrimidines, evolve independently.


http://front.math.ucdavis.edu/math.PR/0510034

---------------------------------------------------------------

3676. HARMONIC MOMENTS OF NON HOMOGENEOUS BRANCHING PROCESSES

Didier Piau

We study the harmonic moments of Galton-Watson processes, possibly non
homogeneous, with positive values. Good estimates of these are needed to
compute unbiased estimators for non canonical branching
  Markov processes, which occur, for instance, in the modeling of the  
polymerase
chain reaction. By convexity, the ratio of the harmonic mean to the  
mean is at
most 1. We prove that, for every square integrable branching  
mechanisms, this
ratio lies between 1-A/k and 1-B/k for every initial population of  
size k
greater than A. The positive constants A and B, such that B is at  
most A, are
explicit and depend only on the generation-by-generation branching  
mechanisms.
In particular, we do not use the distribution of the limit of the  
classical
martingale associated to the Galton-Watson process. Thus, emphasis is  
put on
non asymptotic bounds and on the dependence of the harmonic mean upon  
the size
of the initial population. In the Bernoulli case, which is relevant  
for the
modeling of the polymerase chain reaction, we prove essentially  
optimal bounds
that are valid for every initial population. Finally, in the general  
case and
for large enough initial populations, similar techniques yield sharp  
estimates
of the harmonic moments of higher degrees.


http://front.math.ucdavis.edu/math.PR/0510035

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3677. INVARIANCE PRINCIPLE FOR THE COVERAGE RATE OF GENOMIC PHYSICAL  
MAPPINGS

Didier Piau

We study some stochastic models of physical mapping of genomic  
sequences. Our
starting point is a global construction of the process of the clones  
and of the
process of the anchors which are used to map the sequence. This  
yields explicit
formulas for the moments of the proportion occupied by the anchored  
clones,
even in inhomogeneous models. This also allows to compare, in this  
respect,
inhomogeneous models to homogeneous ones. Finally, for homogeneous  
models, we
provide nonasymptotic bounds of the variance and we prove functional  
invariance
results.


http://front.math.ucdavis.edu/math.PR/0510036

---------------------------------------------------------------

3678. ASYMPTOTICS OF ITERATED BRANCHING PROCESSES

Didier Piau

We study the iterated Galton-Watson process (IGW), possibly with  
thinning,
introduced by Gawe{\l}and Kimmel to model the number of repeats of  
DNA triplets
during some genetic disorders. If the process involves some thinning,  
then
extinction and explosion can have positive probability  
simultaneously. If the
underlying (simple) Galton-Watson process is nondecreasing with mean  
m, then,
conditionally on the explosion, the logarithm of the population of  
the IGW at
time n+1 is equivalent to log(m) times the population at time n,  
almost surely.
This simplifies arguments of Gawe{\l}and Kimmel, and confirms and  
extends a
conjecture of Pakes.


http://front.math.ucdavis.edu/math.PR/0510037

---------------------------------------------------------------

3679. ON TWO DUALITY PROPERTIES OF RANDOM WALKS IN RANDOM ENVIRONMENT  
ON  THE INTEGER LINE

Didier Piau

According to Comets, Gantert and Zeitouni on the one hand and to  
Derriennic
on the other hand, some functionals associated to the hitting times  
of random
walks in random environment on the integer line coincide, for the  
walk itself
and for the walk in the reversed environment. We show that these two  
duality
principles are algebraically equivalent, that they both stem from the  
Markov
property of the walk in a fixed environment, and not of the  
ergodicity of the
model, and that there exists finitist and almost sure versions of  
this duality.


http://front.math.ucdavis.edu/math.PR/0510038

---------------------------------------------------------------

3680. COUNTING THE CHAIN RECORDS: THE PRODUCT CASE

Alexander V. Gnedin

Chain records is a new type of multidimensional record. We discuss  
how often
the chain records are broken when the background sampling is from the  
unit cube
with uniform distribution (or, more generally, from an arbitrary  
continuous
product distribution).


http://front.math.ucdavis.edu/math.PR/0510042

---------------------------------------------------------------

3681. MAXIMAL GENERALIZATION OF BAUM-KATZ THEOREM AND OPTIMALITY OF   
SEQUENTIAL TESTS

Didier Piau

Baum-Katz theorem asserts that the Cesaro means of i.i.d. increments
distributed like X r-converge if and only if |X|^{r+1} is integrable. We
generalize this, and we unify other results, by proving that the  
following
equivalence holds, if and only if G is moderate: the Cesaro means G- 
converge if
and only if G(L(a)) is integrable for every a if and only if |X|.G(| 
X|) is
integrable. Here, L(a) is the last time when the deviation of the  
Cesaro mean
from its limit exceeds a, and G-convergence is the analogue of r- 
convergence.
This solves a question about the asymptotic optimality of Wald's  
sequential
tests.


http://front.math.ucdavis.edu/math.PR/0510043

---------------------------------------------------------------

3682. SELF-AVERAGING PROPERTY OF QUEUING SYSTEMS

Alexandre Rybko and  Senya Shlosman and Alexandre Vladimirov

We establish the averaging property for a queuing process with one  
server,
M(t)/GI/1. It is a new relation between the output flow rate and the  
input flow
rate, crucial in the study of the Poisson Hypothesis. Its  
implications include
the statement that the output flow always possesses more regularity  
than the
input flow.


http://front.math.ucdavis.edu/math.PR/0510046

---------------------------------------------------------------

3683. THE LOCALIZED PHASE OF DISORDERED COPOLYMERS WITH ADSORPTION

G. Giacomin (1) and  F. L. Toninelli (2) ((1) Universite' de Paris 7  
and   (2) ENS Lyon, UMR--CNRS 5672)

We analyze the localized phase of a general model of a directed  
polymer in
the proximity of an interface that separates two solvents. Each  
monomer unit
carries a charge, $\omega_n$, that determines the type (attractive or
repulsive) and the strength of its interaction with the solvents. In  
addition,
there is a polymer--interface interaction and we want to model the  
case in
which there are impurities $\tilde\omega_n$, that we call again  
charges, at the
interface. The charges are distributed in an in--homogeneous fashion  
along the
chain and at the interface: more precisely the model we consider is  
of quenched
disordered type.
   It is well known that such a model undergoes a localization/ 
delocalization
transition. We focus on the localized phase, where the polymer sticks  
to the
interface. Our new results include estimates on the exponential decay of
averaged correlations and the proof that the free energy is infinitely
differentiable away from the transition. Other results we prove,  
instead,
generalize earlier works that typically deal either with the case of  
copolymers
near an homogeneous interface ($\tilde\omega\equiv 0$) or with the  
case of
disordered pinning, where the only polymer--environment interaction  
is at the
interface ($\omega\equiv 0$). Moreover, with respect to most of the  
previous
literature, we work with rather general distributions of charges (we  
will
assume only a suitable concentration inequality).


http://front.math.ucdavis.edu/math.PR/0510047

---------------------------------------------------------------

3684. ON INVARIANCE OF DOMAINS WITH SMOOTH BOUNDARIES WITH RESPECT  
TO  STOCHASTIC DIFFERENTIAL EQUATIONS

Vitalii A. Gasanenko

We prove constructible sufficient conditions of lack of exit by  
solutions of
stochastic differential Ito's equations from domains with smooth  
boundaries


http://front.math.ucdavis.edu/math.PR/0510077

---------------------------------------------------------------

3685. ON A STOCHASTIC PARTIAL DIFFERENTIAL EQUATION WITH NON-LOCAL  
DIFFUSION

Pascal Azerad (I3M) and  Mohamed Mellouk (I3M)

In this paper, we prove existence, uniqueness and regularity for a  
class of
stochastic partial differential equations with a fractional Laplacian  
driven by
a space-time white noise in dimension one. The equation we consider  
may also
include a reaction term.


http://front.math.ucdavis.edu/math.AP/0510107

---------------------------------------------------------------

3686. RANDOM WALK IN DYNAMIC MARKOVIAN RANDOM ENVIRONMENT

Antar Bandyopadhyay and Ofer Zeitouni

We consider a model, introduced by Boldrighini, Minlos and  
Pellegrinotti, of
random walks in dynamical random environments on the integer lattice  
Z^d with
d>=1. In this model, the environment changes over time in a Markovian  
manner,
independently across sites, while the walker uses the environment at its
current location in order to make the next transition. In contrast  
with the
cluster expansions approach of Boldrighini, Minlos and Pellegrinotti,  
we follow
a probabilistic argument based on regeneration times. We prove an  
annealed SLLN
and invariance principle for any dimension, and provide a quenched  
invariance
principle for dimension d > 6, providing for d>6 an alternative to the
analytical approach of Boldrighini, Minlos and Pellegrinotti, with  
the added
benefit that it is valid under weaker assumptions. The quenched  
results use, in
addition to the regeneration times already mentioned, a technique  
introduced by
Bolthausen and Sznitman.


http://front.math.ucdavis.edu/math.PR/0509066

---------------------------------------------------------------

3687. A FREE ANALOGUE OF SHANNON'S PROBLEM ON MONOTONICITY OF ENTROPY

D. Shlyakhtenko

We prove a free probability analog of a result of
Artstein-Bally-Barthez-Naor. In particualar we prove that if X_{1},X_ 
{2},...
are freely independent identically distributed random variables, then  
the free
entropy chi(X_{1}+...+X_{n}/\sqrt{n}) is monotone increasing for all  
n. Our
proof also leads to a slight simplification of the original argument  
in the
classical case.


http://front.math.ucdavis.edu/math.OA/0510103

---------------------------------------------------------------

3688. TAIL ASYMPTOTICS FOR THE SUPREMUM OF AN INDEPENDENT  
SUBADDITIVE  PROCESS, WITH APPLICATIONS TO MONOTONE-SEPARABLE NETWORKS

Marc Lelarge

Tail asymptotics for the supremum of an independent subadditive  
process are
obtained as a function of the logarithmic moment generating function.  
We use
this analysis to obtain large deviations results for queueing  
networks in their
stationary regime. In the particular case of (max,plus)-linear  
recursions, the
rate of exponential decay of the stationary solution can be explicitly
computed.


http://front.math.ucdavis.edu/math.PR/0510117

---------------------------------------------------------------

3689. ENTROPIC REPULSION FOR A CLASS OF GAUSSIAN INTERFACE MODELS IN  
HIGH  DIMENSIONS

Noemi Kurt

Consider the centered Gaussian field on the lattice $\mathbb{Z}^d,$ $d 
$ large
enough, with covariances given by the inverse of $\sum_{j=k}^K q_j(- 
\Delta)^j,$
where $\Delta$ is the discrete Laplacian and $\{q_j\}_{k\leq j\leq K} 
$ is a
polynomial satisfying certain additional conditions. We extend a  
previously
known result to show that the probability that all spins are  
nonnegative on a
box of side-length $N$ has an exponential decay at rate of order
$N^{d-2k}\log{N}.$ We are able to explicitly compute the constant,  
which is
given in terms of a higher-order capacity of the unit cube, analogous  
to the
known result for the lattice free field.


http://front.math.ucdavis.edu/math.PR/0510143

---------------------------------------------------------------

3690. Q-GAUSSIAN DISTRIBUTIONS. ON CALCULUS OF MEAURES  
ORTHOGONALIZING  Q-HERMITE POLYNOMIALS

Pawe{\l} J. Szab{\l}owki

We present some properties of measures orthogonalizing set of q-Hermite
polynomials so called $q$-Gaussian measures. We also present an  
algorithm
simmulating i.i.d. sequencs of random variables having $q$-Gaussian
distribution.


http://front.math.ucdavis.edu/math.PR/0510153

---------------------------------------------------------------

3691. DISTRIBUTION OF PSEUDO-CRITICAL TEMPERATURES AND LACK OF SELF- 
AVERAGING   IN DISORDERED POLAND-SCHERAGA MODELS WITH DIFFERENT LOOP  
EXPONENTS

Cecile Monthus and Thomas Garel

According to recent progresses in the finite size scaling theory of
disordered systems, thermodynamic observables are not self-averaging at
critical points when the disorder is relevant in the Harris criterion  
sense.
This lack of self-averageness at criticality is directly related to the
distribution of pseudo-critical temperatures $T_c(i,L)$ over the  
ensemble of
samples $(i)$ of size $L$. In this paper, we apply this analysis to  
disordered
Poland-Scheraga models with different loop exponents $c 
$,corresponding to
marginal and relevant disorder. In all cases, we numerically obtain a  
Gaussian
histogram of pseudo-critical temperatures $T_c(i,L)$ with mean $T_c^ 
{av}(L)$
and width $\Delta T_c(L)$. For the marginal case $c=1.5$  
corresponding to
two-dimensional wetting, both the width $\Delta T_c(L)$ and the shift
$[T_c(\infty)-T_c^{av}(L)]$ decay as $L^{-1/2}$, so the exponent is  
unchanged
($\nu_{random}=2=\nu_{pure}$) but disorder is relevant and leads to non
self-averaging at criticality. For relevant disorder $c=1.75$, the width
$\Delta T_c(L)$ and the shift $[T_c(\infty)-T_c^{av}(L)]$ decay with  
the same
new exponent $L^{-1/\nu_{random}}$ (where $\nu_{random} \sim 2.7 > 2 >
\nu_{pure}$) and there is again no self-averaging at criticality.  
Finally for
the value $c=2.15$, of interest in the context of DNA denaturation, the
transition is first-order in the pure case. In the presence of  
disorder, the
width $\Delta T_c(L) \sim L^{-1/2}$ dominates over the shift
$[T_c(\infty)-T_c^{av}(L)] \sim L^{-1}$, i.e. there are two  
correlation length
exponents $\nu=2$ and $\tilde \nu=1$ that govern respectively the
averaged/typical loop distribution.


http://front.math.ucdavis.edu/cond-mat/0509479

---------------------------------------------------------------

3692. PARTIAL FILLUP AND SEARCH TIME IN LC TRIES

Svante Janson and Wojciech Szpankowski

Andersson and Nilsson introduced in 1993 a level-compressed trie (in  
short:
LC trie) in which a full subtree of a node is compressed to a single  
node of
degree being the size of the subtree. Recent experimental results  
indicated a
'dramatic improvement' when full subtrees are replaced by partially  
filled
subtrees. In this paper, we provide a theoretical justification of these
experimental results showing, among others, a rather moderate  
improvement of
the search time over the original LC tries. For such an analysis, we  
assume
that n strings are generated independently by a binary memoryless  
source with p
denoting the probability of emitting a 1. We first prove that the so  
called
alpha-fillup level (i.e., the largest level in a trie with alpha  
fraction of
nodes present at this level) is concentrated on two values with high
probability. We give these values explicitly up to O(1), and observe  
that the
value of alpha (strictly between 0 and 1) does not affect the leading  
term.
   This result directly yields the typical depth (search time) in the  
alpha-LC
tries with p not equal to 1/2, which turns out to be C loglog n for an
explicitly given constant C (depending on p but not on alpha). This  
should be
compared with recently found typical depth in the original LC tries  
which is C'
loglog n for a larger constant C'. The search time in alpha-LC tries  
is thus
smaller but of the same order as in the original LC tries.


http://front.math.ucdavis.edu/cs.DS/0510017

---------------------------------------------------------------

3693. FROM GUMBEL TO TRACY-WIDOM

Kurt Johansson

The Tracy-Widom distribution that has been much studied in recent  
years can
be thought of as an extreme value distribution. We discuss interpolation
between the classical extreme value distribution $\exp(-\exp(-x))$,  
the Gumbel
distribution and the Tracy-Widom distribution. There is a family of
determinantal processes whose edge behaviour interpolates between a  
Poisson
process with density $\exp(-x)$ and the Airy kernel point process.  
This process
can be obtained as a scaling limit of a grand canonical version of a  
random
matrix model introduced by Moshe, Neuberger and Shapiro. We also  
consider the
deformed GUE ensemble, $M=M_0+\sqrt{2S} V$, with $M_0$ diagobal with
independent elements and $V$ from GUE. Here we do not see a  
transition from
Tracy-Widom to Gumbel, but rather a transition from Tracy-Widom to  
Gaussian.


http://front.math.ucdavis.edu/math.PR/0510181

---------------------------------------------------------------

3694. SELF-INTERSECTION TIMES FOR RANDOM WALK, AND RANDOM WALK IN  
RANDOM  SCENERY

Amine Asselah (LATP) and  Fabienne Castell (LATP)

We consider Random Walk in Random Scenery, denoted $X\_n$, where the  
random
walk is symmetric on $Z^d$, with $d>4$, and the random field is made  
up of
i.i.d random variables with a stretched exponential tail decay, with  
exponent
$\alpha$ with $1<\alpha$. We present asymptotics for the probability,  
over both
randomness, that $\{X\_n>n^{\beta}\}$ for $1/2<\beta<1$. To obtain such
asymptotics, we establish large deviations estimates for the the
self-intersection local times process.


http://front.math.ucdavis.edu/math.PR/0510190

---------------------------------------------------------------

3695. RANDOM MATRICES AND DETERMINANTAL PROCESSES

Kurt Johansson

We survey recent results on determinantal processes, random growth,  
random
tilings and their relation to random matrix theory.


http://front.math.ucdavis.edu/math-ph/0510038

---------------------------------------------------------------

3696. QUANTUM DIFFUSION, MEASUREMENT AND FILTERING

V.P.Belavkin

A brief presentation of the basic concepts in quantum probability  
theory is
given in comparison to the classical one. The notion of quantum white  
noise,
its explicit representation in Fock space, and necessary results of
noncommutative stochastic analysis and integration are outlined.  
Algebraic
differential equations that unify the quantum non Markovian diffusion  
with
continuous non demolition observation are derived. A stochastic  
equation of
quantum diffusion filtering generalising the classical Markov filtering
equation to the quantum flows over arbitrary *-algebra is obtained. A  
Gaussian
quantum diffusion with one dimensional continuous observation is  
considered.The
a posteriori quantum state difusion in this case is reduced to a  
linear quantum
stochastic filter equation of Kalman-Bucy type and to the operator  
Riccati
equation for quantum correlations. An example of continuous  
nondemolition
observation of the coordinate of a free quantum particle is considered,
describing a continuous collase to the stationary solution of the linear
quantum filtering problem found in the paper.


http://front.math.ucdavis.edu/quant-ph/0510028

---------------------------------------------------------------

3697. THE BI-POISSON PROCESS: A QUADRATIC HARNESS

Wlodzimierz Bryc and  Wojciech Matysiak and  Jacek Wesolowski

This paper is a continuation of our previous research on quadratic  
harnesses,
i.e. processes with linear regressions and quadratic conditional  
variances. In
this paper we define the class of orthogonal polynomials that is a
two-parameter extension of the Al-Salam--Chihara polynomials, we  
derive a
relation between these polynomials for different values of  
parameters, and we
use the relation to construct a new class of quadratic harnesses. A  
special
case of our construction is a simple transformation of a linear pure- 
birth
process with immigration followed by a linear pure death process.


http://front.math.ucdavis.edu/math.PR/0510208

---------------------------------------------------------------

3698. MARKOV CHAINS IN A DIRICHLET ENVIRONMENT AND HYPERGEOMETRIC  
INTEGRALS

Christophe Sabot (UMPA-ENSL)

The aim of this text is to establish some relations between Markov  
chains in
Dirichlet Environments on directed graphs and certain hypergeometric  
integrals
associated with a particular arrangement of hyperplanes. We deduce  
from these
relations and the computation of the connexion obtained by moving one
hyperplane of the arrangement some new relations on important  
functionals of
the Markov chain.


http://front.math.ucdavis.edu/math.PR/0510236

---------------------------------------------------------------

3699. LARGE DEVIATIONS FOR THE ZERO SET OF AN ANALYTIC FUNCTION WITH  
DIFFUSING  COEFFICIENTS

J. Ben Hough

The "hole probability" that the zero set of the time dependent planar
Gaussian analytic function f(z,t) = sum_(n=0)^infty a_n(t) z^n/sqrt 
(n!), where
a_n(t) are i.i.d. complex valued Ornstein-Uhlenbeck processes, does not
intersect a disk of radius R for all 0<t<T decays like exp(-Te^ 
(cR^2)). This
result sharply differentiates the zero set of f from a number of  
canonical
evolving planar point processes. For example, the hole probability of  
the
perturbed lattice model {sqrt{\pi}(m,n) + c zeta_{m,n}: m,n integers}  
where
zeta_(m,n) are i.i.d. Ornstein-Uhlenbeck processes decays like exp(- 
cTR^4).
This stark contrast is also present in the "overcrowding probability"  
that a
disk of radius R contains at least N zeros for all 0<t<T.


http://front.math.ucdavis.edu/math.PR/0510237

---------------------------------------------------------------

3700. DISTRIBUTIONAL TRANSFORMATIONS, ORTHOGONAL POLYNOMIALS, AND  
STEIN  CHARACTERIZATIONS

Larry Goldstein and  Gesine Reinert

A new class of distributional transformations is introduced,  
characterized by
equations relating function weighted expectations of test functions  
on a given
distribution to expectations of the transformed distribution on the test
function's higher order derivatives. The class includes the size and  
zero bias
transformations, and when specializing to weighting by polynomial  
functions,
relates distributional families closed under independent addition,  
and in
particular the infinitely divisible distributions, to the family of
transformations induced by their associated orthogonal polynomial  
systems. For
these families, generalizing a well known property of size biasing,  
sums of
independent variables are transformed by replacing summands chosen  
according to
a multivariate distribution on its index set by independent variables  
whose
distributions are transformed by members of that same family. A  
variety of the
transformations associated with the classical orthogonal polynomial  
systems
have as fixed points the original distribution, or a member of the  
same family
with different parameter.


http://front.math.ucdavis.edu/math.PR/0510240

---------------------------------------------------------------

3701. TWO CHOICE OPTIMAL STOPPING

David Assaf and  Larry Goldstein and Ester Samuel-Cahn

Let $X_n,...,X_1$ be i.i.d. random variables with distribution  
function $F$.
A statistician, knowing $F$, observes the $X$ values sequentially and  
is given
two chances to choose $X$'s using stopping rules. The statistician's  
goal is to
stop at a value of $X$ as small as possible. Let $V_n^2$ equal the  
expectation
of the smaller of the two values chosen by the statistician when  
proceeding
optimally. We obtain the asymptotic behavior of the sequence $V_n^2$  
for a
large class of $F$'s belonging to the domain of attraction (for the  
minimum)
${\cal D}(G^\alpha)$, where $G^\alpha(x)=[1-\exp(-x^\alpha)]{\bf I}(x  
\ge 0)$.
The results are compared with those for the asymptotic behavior of the
classical one choice value sequence $V_n^1$, as well as with the  
``prophet
value" sequence $V_n^p=E(\min\{X_n,...,X_1\})$.


http://front.math.ucdavis.edu/math.PR/0510242

---------------------------------------------------------------

3702. DEVIATIONS BOUNDS AND CONDITIONAL PRINCIPLES FOR THIN SETS

Patrick Cattiaux (MODAL'X and  CMAP) and  Nathael Gozlan (MODAL'X)

The aim of this paper is to use non asymptotic bounds for the  
probability of
rare events in the Sanov theorem, in order to study the asymptotics in
conditional limit theorems (Gibbs conditioning principle for thin sets).
Applications to stochastic mechanics or calibration problems for  
diffusion
processes are discussed.


http://front.math.ucdavis.edu/math.PR/0510257

---------------------------------------------------------------

3703. HYPERCONTRACTIVITY FOR PERTURBED DIFFUSION SEMIGROUPS

Patrick Cattiaux (MODAL'X and  CMAP)

$\mu$ being a nonnegative measure satisfying some log-Sobolev  
inequality, we
give conditions on F for the measure $\nu=e^{-2F} \mu$ to also  
satisfy some
log-Sobolev inequality. Explicit examples are studied.


http://front.math.ucdavis.edu/math.PR/0510258

---------------------------------------------------------------

3704. CURRENT LARGE DEVIATIONS FOR ASYMMETRIC EXCLUSION PROCESSES  
WITH OPEN   BOUNDARIES

T. Bodineau and  B. Derrida

We study the large deviation functional of the current for the Weakly
Asymmetric Simple Exclusion Process in contact with two reservoirs.We  
compare
this functional in the large drift limit to the one of the Totally  
Asymmetric
Simple Exclusion Process, in particular to the Jensen-Varadhan  
functional.
Conjectures for generalizing the Jensen-Varadhan functional to open  
systems are
also stated.


http://front.math.ucdavis.edu/cond-mat/0509179

---------------------------------------------------------------

3705. LOWER LIMITS AND EQUIVALENCES FOR CONVOLUTION TAILS

Serguei Foss and  Dmitry Korshunov

Suppose $F$ is a distribution on the half-line $[0,\infty)$. We study  
the
limits of the ratios of tails $\bar{F*F}(x)/\bar F(x)$ as $x\to\infty 
$. We also
discuss the classes of distributions ${\mathcal S}$, ${\mathcal S} 
(\gamma)$,
and ${\mathcal S}^*$.


http://front.math.ucdavis.edu/math.PR/0510273

---------------------------------------------------------------

3706. RECURSIVE PARTITION STRUCTURES

A.V. Gnedin and Yu. Yakubovich

A class of random discrete distributions $P$ is introduced by means of a
recursive splitting of unity. Assuming supercritical branching, we  
show that
for partitions induced by sampling from such $P$ a power growth of  
the number
of blocks is typical. Some known and some new partition structures  
appear when
$P$ is induced by a Dirichlet splitting.


http://front.math.ucdavis.edu/math.PR/0510305

---------------------------------------------------------------

3707. HOW FAST IS THE BANDIT?

Damien Lamberton (LAMA) and  Gilles Pag\`{e}s (PMA)

In this paper we investigate the rate of convergence of the so-called
two-armed bandit algorithm in a financial context of asset  
allocation. The
behaviour of the algorithm turns out to be highly non-standard: no  
CLT whatever
the time scale, possible existence of two rate regimes.


http://front.math.ucdavis.edu/math.PR/0510351

---------------------------------------------------------------

3708. ORGANIZED VERSUS SELF-ORGANIZED CRITICALITY IN THE ABELIAN  
SANDPILE  MODEL

A. Fey-den Boer and F. Redig

We define stabilizability of an infinite volume height configuration  
and of a
probability measure on height configurations. We show that for high  
enough
densities, a probability measure cannot be stabilized. We also show  
that in
some sense the thermodynamic limit of the uniform measures on the  
recurrent
configurations of the abelian sandpile model (ASM) is a maximal  
element of the
set of stabilizable measures. In that sense the self-organized critical
behavior of the ASM can be understood in terms of an ordinary transition
between stabilizable and non-stabilizable


http://front.math.ucdavis.edu/math-ph/0510060

---------------------------------------------------------------

3709. WHAT DOES A GENERIC MARKOV OPERATOR LOOK LIKE

A.Vershik

We consider generic i.e., forming an everywhere dense massive subset  
classes
of Markov operators in the space $L^2(X,\mu)$ with a finite  
continuous measure.
Since there is a canonical correspondence that associates with each  
Markov
operator a multivalued measure-preserving transformation (i.e., a
polymorphism), as well as a stationary Markov chain, we can also  
speak about
generic polymorphisms and generic Markov chains. The most important and
inexpected generic properties of Markov operators (or Markov chains or
polymorphisms) is nonmixing and totally nondeterministicity. It was  
not known
even existence of such Markov operators (the first example due to
M.Rozenblatt). We suppose that this class coinsided with the class of  
special
random perturbations of $K$-automorphisms. This theory is measure  
theoretic
counterpart of the theory of nonselfadjoint contractions and its  
application.


http://front.math.ucdavis.edu/math.FA/0510320

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3710. ROUNDING OF CONTINUOUS RANDOM VARIABLES AND OSCILLATORY  
ASYMPTOTICS

Svante Janson

Let X be a continuous random variable. We study the characteristic  
function
and moments of the integer-valued random variable obtained by  
rounding X+a to
the nearest smallest integer, where a is a constant. The results can be
regarded as exact versions of Sheppard's correction.
   Rounded variables of this type often occur as subsequence limits  
of sequences
of integer-valued random variable. This leads to oscillatory terms in
asymptotics for these variables, something that often has been  
observed, for
example in the analysis of several algorithms. We give some examples,  
including
applications to tries, digital search trees and Patricia tries.


http://front.math.ucdavis.edu/math.PR/0509009

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3711. ABSOLUTELY CONTINUOUS, INVARIANT MEASURES FOR DISSIPATIVE,  
ERGODIC  TRANSFORMATIONS

Jon. Aaronson and  Tom Meyerovitch

We show that a dissipative, ergodic measure preserving transformation  
of a
sigma-finite, non-atomic measure space always has many non-proportional,
absolutely continuous, invariant measures and is ergodic with respect  
to each
one of these.


http://front.math.ucdavis.edu/math.DS/0509093

---------------------------------------------------------------

3712. A THEOREM ON MAJORIZING MEASURES

Witold Bednorz

We prove that whenever there exists a majroizing measure on the  
metric space,
then each process with bounded increments has necessarily bounded  
samples. This
is a strengthening of one the main results in Talagrand's paper "Sample
boundedness of stochastic processes under increment conditions".


http://front.math.ucdavis.edu/math.PR/0510373

---------------------------------------------------------------

3713. A PENALIZED BANDIT ALGORITHM

Damien Lamberton (LAMA) and  Gilles Pag\`{e}s (PMA)

We study a two armed-bandit algorithm with penalty. We show the  
convergence
of the algorithm and establish the rate of convergence. For some  
choices of the
parameters, we obtain a central limit theorem in which the limit  
distribution
is characterized as the unique stationary distribution of a  
discontinuous
Markov process.


http://front.math.ucdavis.edu/math.PR/0510384

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3714. PHASE TRANSITION IN THE ALDOUS-SHIELDS MODEL OF GROWING TREES

Davis S. Dean and Satya N. Majumdar

We study analytically the late time statistics of the number of  
particles in
a growing tree model introduced by Aldous and Shields. In this model,  
a cluster
grows in continuous time on a binary Cayley tree, starting from the  
root, by
absorbing new particles at the empty perimeter sites at a rate  
proportional to
c^{-l} where c is a positive parameter and l is the distance of the  
perimeter
site from the root. For c=1, this model corresponds to random binary  
search
trees and for c=2 it corresponds to digital search trees in computer  
science.
By introducing a backward Fokker-Planck approach, we calculate the  
mean and the
variance of the number of particles at large times and show that the  
variance
undergoes a `phase transition' at a critical value c=sqrt{2}. While for
c>sqrt{2} the variance is proportional to the mean and the  
distribution is
normal, for c<sqrt{2} the variance is anomalously large and the  
distribution is
non-Gaussian due to the appearance of extreme fluctuations. The model is
generalized to one where growth occurs on a tree with $m$ branches  
and, in this
more general case, we show that the critical point occurs at c=sqrt{m}.


http://front.math.ucdavis.edu/cond-mat/0510429

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3715. BALLISTIC RANDOM WALK IN A RANDOM ENVIRONMENT WITH A FORBIDDEN  
DIRECTION

F. Rassoul-Agha and T. Seppalainen

We consider a ballistic random walk in an i.i.d. random environment  
that does
not allow retreating in a certain fixed direction. Homogenization and
regeneration techniques combine to prove a law of large numbers and  
an averaged
invariance principle. The assumptions are non-nestling and $1+\e$  
(resp.\
$2+\e$) moments for the step of the walk uniformly in the  
environment, for the
law of large numbers (resp. invariance principles). We also investigate
invariance principles under fixed environments, and invariance  
principles for
the environment-dependent mean of the walk.


http://front.math.ucdavis.edu/math.PR/0510392

---------------------------------------------------------------

3716. A MODEL FOR THE BUS SYSTEM IN CUERNEVACA (MEXICO)

Jinho Baik and  Alexei Borodin and  Percy Deift and Toufic Suidan

The bus transportation system in Cuernevaca, Mexico, has certain
distinguished, innovative features and has been the subject of an  
intriguing,
recent study by M. Krbalek and P. Seba. Krbalek and Seba analyzed the
statistics of bus arrivals on Line 4 close to the city center. They  
studied, in
particular, the bus spacing distribution and also the bus number  
variance
measuring the fluctuations of the total number of buses arriving at a  
fixed
location during a time interval T. Quite remarkably, it was found  
that these
two statistics are well modeled by the Gaussian Unitary Ensemble  
(GUE) of
random matrix theory. Our goal in this paper is to provide a plausible
explanation of these observations, and to this end we introduce a  
microscopic
model for the bus line that leads simply and directly to GUE.


http://front.math.ucdavis.edu/math.PR/0510414

---------------------------------------------------------------

3717. THE ONSET OF DOMINANCE IN BALLS-IN-BINS PROCESSES WITH FEEDBACK

Roberto Oliveira and Joel Spencer

Consider a balls-in-bins process in which each new ball goes into a  
given bin
with probability proportional to $f(n)$, where $n$ is the number of  
balls
currently in the bin and $f$ is a fixed positive function. It is  
known that
these so-called {\em balls-in-bins processes with feedback} have a  
monopolistic
regime: if $f(x)=x^p$ for $p>1$, then there is a finite time after  
which one of
the bins will receive all incoming balls.
   Our goal in this paper is to quantify the onset of monopoly. We  
show that the
initial number of balls is large and bin 1 starts with a fraction $ 
\alpha>1/2$
of the balls, then with very high probability its share of the total  
number of
balls never decreases significantly below $\alpha$. Thus a bin that  
obtains
more than half of the balls at a "large time" will most likely  
preserve its
position of leadership. However, the probability that the winning bin  
has a
non-negligible advantage after $n$ balls are in the system is
$\sim{const.}\times n^{1-p}$, and the number of balls in the losing  
bin has a
power-law tail. Similar results also hold for more general functions  
$f$.


http://front.math.ucdavis.edu/math.PR/0510415

---------------------------------------------------------------

3718. COUNTABLE STATE SHIFTS AND UNIQUENESS OF G-MEASURES

Anders Johansson and  Anders \"Oberg and Mark Pollicott

In this paper we present a new approach to studying g-measures which  
is based
upon local absolute continuity. We extend the result in [11] that square
summability of variations of g-functions ensures uniqueness of g- 
measures. The
first extension is to the case of countably many symbols. The second  
extension
is to some cases where $g \geq 0$, relaxing the earlier requirement  
in [11]
that inf g>0.


http://front.math.ucdavis.edu/math.DS/0509109

---------------------------------------------------------------

3719. AN ERROR BOUND IN THE SUDAKOV-FERNIQUE INEQUALITY

Sourav Chatterjee

We obtain an asymptotically sharp error bound in the classical
Sudakov-Fernique comparison inequality for finite collections of  
gaussian
random variables. Our proof is short and self-contained, and gives an  
easy
alternative argument for the classical inequality, extended to the  
case of
non-centered processes.


http://front.math.ucdavis.edu/math.PR/0510424

---------------------------------------------------------------

3720. ESTIMATES FOR THE DENSITY OF A NONLINEAR LANDAU PROCESS

H\'{e}l\`{e}ne Gu\'{e}rin (IRMAR) and  Sylvie M\'{e}l\'{e}ard  
(MODAL'X) and   Eulalia Nualart (LAGA)

The aim of this paper is to obtain estimates for the density of the  
law of a
specific nonlinear diffusion process at any positive bounded time.  
This process
is issued from kinetic theory and is called Landau process, by  
analogy with the
associated deterministic Fokker-Planck-Landau equation. It is not  
Markovian,
its coefficients are not bounded and the diffusion matrix is degenerate.
Nevertheless, the specific form of the diffusion matrix and the  
nonlinearity
imply the non-degeneracy of the Malliavin matrix and then the  
existence and
smoothness of the density. In order to obtain a lower bound for the  
density,
the known results do not apply. However, our approach follows the  
main idea
consisting in discretizing the interval time and developing a  
recursive method.
To this aim, we prove and use refined results on conditional Malliavin
calculus. The lower bound implies the positivity of the solution of  
the Landau
equation, and partially answers to an analytical conjecture. We also  
obtain an
upper bound for the density, which again leads to an unusual estimate  
due to
the bad behavior of the coefficients.


http://front.math.ucdavis.edu/math.PR/0510439

---------------------------------------------------------------

3721. CONNECTIVITY TRANSITIONS IN NETWORKS WITH SUPER-LINEAR  
PREFERENTIAL  ATTACHMENT

Roberto Oliveira and Joel Spencer

We analyze an evolving network model of Krapivsky and Redner in which  
new
nodes arrive sequentially, each connecting to a previously existing  
node b with
probability proportional to the p-th power of the in-degree of b. We  
restrict
to the super-linear case p>1. When 1+1/k< p \leq 1 + 1/(k-1) the  
structure of
the final countable tree is determined. There is a finite tree T with
distinguished v (which has a limiting distribution) on which is  
"glued" a
specific infinite tree. v has an infinite number of children, an  
infinite
number of which have k-1 children, and there are only a finite number  
of nodes
(possibly only v) with k or more children. Our basic technique is to  
embed the
discrete process in a continuous time process using exponential random
variables, a technique that has previously been employed in the study of
balls-in-bins processes with feedback.


http://front.math.ucdavis.edu/math.PR/0510446

---------------------------------------------------------------

3722. INDIVIDUAL-BASED PROBABILISTIC MODELS OF ADAPTIVE EVOLUTION AND  
VARIOUS  SCALING APPROXIMATIONS

Nicolas Champagnat (MODAL'X) and  R\'{e}gis Ferri\`{e}re and  Sylvie   
M\'{e}l\'{e}ard (MODAL'X)

We are interested in modelling Darwinian evolution, resulting from the
interplay of phenotypic variation and natural selection through  
ecological
interactions. Our models are rooted in the microscopic, stochastic  
description
of a population of discrete individuals characterized by one or several
adaptive traits. The population is modelled as a stochastic point  
process whose
generator captures the probabilistic dynamics over continuous time of  
birth,
mutation, and death, as influenced by each individual's trait values,  
and
interactions between individuals. An offspring usually inherits the  
trait
values of her progenitor, except when a mutation causes the offspring  
to take
an instantaneous mutation step at birth to new trait values. We look for
tractable large population approximations. By combining various  
scalings on
population size, birth and death rates, mutation rate, mutation step,  
or time,
a single microscopic model is shown to lead to contrasting  
macroscopic limits,
of different nature: deterministic, in the form of ordinary,  
integro-, or
partial differential equations, or probabilistic, like stochastic  
partial
differential equations or superprocesses. In the limit of rare  
mutations, we
show that a possible approximation is a jump process, justifying  
rigorously the
so-called trait substitution sequence. We thus unify different points  
of view
concerning mutation-selection evolutionary models.


http://front.math.ucdavis.edu/math.PR/0510453

---------------------------------------------------------------

3723. FUNDAMENTAL MARKOV SYSTEMS

Ivan Werner

We continue development of the theory of Markov systems initiated in
\cite{Wer1}. In this paper, we introduce fundamental Markov systems  
associated
with random dynamical systems.


http://front.math.ucdavis.edu/math.PR/0509120

---------------------------------------------------------------

3724. COUNTING WITHOUT SAMPLING. NEW ALGORITHMS FOR ENUMERATION  
PROBLEMS USING  STATISTICAL PHYSICS

Antar Bandyopadhyay and David Gamarnik

We propose a new type of approximate counting algorithms for the  
problems of
enumerating the number of independent sets and proper colorings in  
low degree
graphs with large girth. Our algorithms are not based on a commonly  
used Markov
chain technique, but rather are inspired by developments in  
statistical physics
in connection with correlation decay properties of Gibbs measures and  
its
implications to uniqueness of Gibbs measures on infinite trees,  
reconstruction
problems and local weak convergence methods.
   On a negative side, our algorithms provide $\epsilon$- 
approximations only to
the logarithms of the size of a feasible set (also known as free  
energy in
statistical physics). But on the positive side, our approach provides
deterministic as opposed to probabilistic guarantee on approximations.
Moreover, for some regular graphs we obtain explicit values for the  
counting
problem. For example, we show that every 4-regular $n$-node graph  
with large
girth has approximately $(1.494...)^n$ independent sets, and in every
$r$-regular graph with $n$ nodes and large girth the number of $q\geq
r+1$-proper colorings is approximately $[q(1-{1\over q})^{r\over 2}]^n 
$, for
large $n$. In statistical physics terminology, we compute explicitly  
the limit
of the log-partition function. We extend our results to random  
regular graphs.
Our explicit results would be hard to derive via the Markov chain  
method.


http://front.math.ucdavis.edu/math.PR/0510471

---------------------------------------------------------------

3725. PATHWISE UNIQUENESS FOR TWO DIMENSIONAL REFLECTING BROWNIAN  
MOTION IN  LIPSCHITZ DOMAINS

Richard F. Bass and Krzysztof Burdzy

We give a simple proof that in a Lipschitz domain in two dimensions with
Lipschitz constant one, there is pathwise uniqueness for the  
Skorokhod equation
governing reflecting Brownian motion.


http://front.math.ucdavis.edu/math.PR/0510473

---------------------------------------------------------------

3726. BINOMIAL-POISSON ENTROPIC INEQUALITIES AND THE M/M/$\INFTY$ QUEUE

Djalil Chafai (LSProba and  Umr181 Inra/Envt)

This article provides entropic inequalities for binomial-Poisson
distributions, derived from the two points space. They describe in  
particular
the exponential dissipation of $\Phi$-entropies along the M/M/$\infty 
$ queue.
This simple queueing process appears as a model of "constant  
curvature", and
plays for the simple Poisson process the role played by the Ornstein- 
Uhlenbeck
process for Brownian Motion. These inequalities are exactly the local
inequalities of the M/M/$\infty$ process. Some of them are recovered by
semigroup interpolation. Additionally, we explore the behaviour of these
entropic inequalities under a particular scaling, which sees the
Ornstein-Uhlenbeck process as a fluid limit of M/M/$\infty$ queues.  
Proofs are
elementary and rely essentially on the development of a "$\Phi$- 
calculus".


http://front.math.ucdavis.edu/math.PR/0510488

---------------------------------------------------------------

3727. ON SOLUTIONS OF FIRST ORDER STOCHASTIC PARTIAL DIFFERENTIAL  
EQUATIONS

K. Hamza and F. C. Klebaner

This note is concerned with an important for modelling question of  
existence
of solutions of stochastic partial differential equations as proper  
stochastic
processes, rather than processes in the generalized sense. We  
consider a first
order stochastic partial differential equations of the form $\pd Ut =  
DW$, and
$\pd Ut-\pd Ux= DW$, where $D$ is a differential operator and $W(t,x) 
$ is a
continuous but non-differentiable function (field).
   We give a necessary and sufficient condition for stochastic  
equations to have
solutions as functions. The result is then applied to the equation  
for a yield
curve. Proofs are based on probability arguments.


http://front.math.ucdavis.edu/math.PR/0510495

---------------------------------------------------------------

3728. OPTIONS ON HEDGE FUNDS UNDER THE HIGH WATER MARK RULE

Marc Atlan (PMA) and  H\'{e}lyette Geman (DRM) and  Marc Yor (PMA)

The rapidly growing hedge fund industry has provided individual and
institutional investors with new investment vehicles and styles of  
management.
It has also brought forward a new form of performance contract: hedge  
fund
managers receive incentive fees which are typically a fraction of the  
fund net
asset value (NAV) above its starting level - a rule known as high  
water mark.
Options on hedge funds are becoming increasingly popular, in  
particular because
they allow investors with limited capital to get exposure to this new  
asset
class. The goal of the paper is to propose a valuation of options on  
hedge
funds which accounts for the high water market rule. Mathematically,  
this
valuation will lead to an interesting use of local times of Brownian  
motion.
Option prices are numerically computed by inversion of their Laplace
transforms.


http://front.math.ucdavis.edu/math.PR/0510497

---------------------------------------------------------------

3729. ANOTHER APPROACH TO BROWNIAN MOTION

Magda Peligrad and Sergey Utev

Braverman, Mallows and Shepp (1995), showed that if the absolute  
moments of
partial sums of i.i.d. symmetric variables are equal to those of normal
variables, then the marginals have normal distribution. This fact  
suggested the
conjecture that probably the absolute moments alone characterize the
homogeneous process with independent increments. In this paper we  
prove a more
general result that gives a positive answer to this conjecture, and  
then apply
it in order to obtain the CLT for a class of dependent random  
variables under a
normalization involving the absolute moments of partial sums.


http://front.math.ucdavis.edu/math.PR/0510513

---------------------------------------------------------------

3730. A STOCHASTIC-VARIATIONAL MODEL FOR SOFT MUMFORD-SHAH SEGMENTATION

Jianhong Shen

In contemporary image and vision analysis, stochastic approaches  
demonstrate
great flexibility in representing and modeling complex phenomena, while
variational-PDE methods gain enormous computational advantages over  
Monte-Carlo
or other stochastic algorithms. In combination, the two can lead to  
much more
powerful novel models and efficient algorithms. In the current work,  
we propose
a stochastic-variational model for soft (or fuzzy) Mumford-Shah  
segmentation of
mixture image patterns. Unlike the classical hard Mumford-Shah  
segmentation,
the new model allows each pixel to belong to each image pattern with  
some
probability. We show that soft segmentation leads to hard  
segmentation, and
hence is more general. The modeling procedure, mathematical analysis,  
and
computational implementation of the new model are explored in detail,  
and
numerical examples of synthetic and natural images are presented.


http://front.math.ucdavis.edu/math.OC/0510485

---------------------------------------------------------------

3731. SLICES OF BROWNIAN SHEET: NEW RESULTS, AND OPEN PROBLEMS

Davar Khoshnevisan

We can view Brownian sheet as a sequence of interacting Brownian  
motions or
slices. Here we present a number of results about the slices of the  
sheet. A
common feature of our results is that they exhibit phase transition. In
addition, a number of open problems are presented.


http://front.math.ucdavis.edu/math.PR/0510518

---------------------------------------------------------------

3732. FLOWS AND FERROMAGNETS

Geoffrey Grimmett

The two-point correlation function of a Potts model on a graph $G$  
may be
expressed in terms of the flow polynomials of `Poissonian' random graphs
derived from $G$ by replacing each edge by a Poisson-distributed  
number of
copies of itself. This fact extends to Potts models the so-called
random-current expansion of the Ising model.


http://front.math.ucdavis.edu/math.PR/0509127

---------------------------------------------------------------

3733. PHASE TRANSITION ASYMPTOTICS FOR RANDOM WALKS ON A STATIONARY  
RANDOM  POTENTIAL

Gerard Ben Arous and  Stanislav Molchanov and  Alejandro F. Ramirez

We describe a universal transition mechanism characterizing the  
passage to an
annealed behavior and to a regime where the fluctuations about this  
behavior
are Gaussian, for the long time asymptotics of the empirical average  
of the
expected value of the number of random walks which branch and  
annihilate on
${\mathbb Z}^d$, with stationary random rates. The random walks are
independent, continuous time rate $2d\kappa$, simple, symmetric, with  
$\kappa
\ge 0$. A random walk at $x\in{\mathbb Z}^d$, binary branches at rate  
$v_+(x)$,
and annihilates at rate $v_-(x)$. The random environment $w$ has  
coordinates
$w(x)=(v_-(x),v_+(x))$ which are i.i.d. We identify a natural way to  
describe
the annealed-Gaussian transition mechanism under mild conditions on  
the rates.
Indeed, we introduce the exponents
$F_\theta(t):=\frac{H_1((1+\theta)t)-(1+\theta)H_1(t)}{\theta}$, and  
assume
that $\frac{F_{2\theta}(t)-F_\theta(t)}{\theta\log(\kappa t+e)}\to 
\infty$ for
$|\theta|>0$ small enough, where $H_1(t):=\log < m(0,t)>$ and $<m(0,t)>$
denotes the average of the expected value of the number of particles  
$m(0,t,w)$
at time $t$ and an environment of rates $w$, given that initially  
there was
only one particle at 0. Then the empirical average of $m(x,t,w)$ over  
a box of
side $L(t)$ has different behaviors: if $ L(t)\ge e^{\frac{1}{d}
F_\epsilon(t)}$ for some $\epsilon >0$ and large enough $t$, a law of  
large
numbers is satisfied; if $ L(t)\ge e^{\frac{1}{d} F_\epsilon (2t)}$  
for some
$\epsilon>0$ and large enough $t$, a CLT is satisfied. These  
statements are
violated if the reversed inequalities are satisfied for some negative
$\epsilon$. Applications to potentials with Weibull, Frechet and double
exponential tails are given.


http://front.math.ucdavis.edu/math.PR/0510519

---------------------------------------------------------------

3734. MAJORIZING MULTIPLICATIVE CASCADES FOR DIRECTED POLYMERS IN  
RANDOM MEDIA

Francis Comets (PMA) and  Vincent Vargas (PMA)

In this note we give upper bounds for the free energy of discrete  
polymers in
random media. The bounds are given by the so-called generalized  
multiplicative
cascades from the statistical theory of turbulence. For the polymer  
model, we
derive that the quenched free energy is different from the annealed  
one in
dimension 1, for any finite temperature and general environment. This  
implies
localization of the polymer.


http://front.math.ucdavis.edu/math.PR/0510525

---------------------------------------------------------------

3735. LIMITING LAWS ASSOCIATED WITH BROWNIAN MOTION PERTURBATED BY  
NORMALIZED  EXPONENTIAL WEIGHTS I

Bernard Roynette (IEC) and  Pierre Vallois (IEC) and  Marc Yor (PMA)

We determine the rate of decay of the expectation Z(t) of some  
multiplicative
functional related to Brownian motion up to time t. This permits to  
prove that
the Wiener measure, penalized by this multiplicative functional,  
converges as t
goes to infinity to a probability measure (p.m.) . We obtain the law  
of the
canonical process under this new p.m.


http://front.math.ucdavis.edu/math.PR/0510550

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3736. A TRACE THEOREM FOR DIRICHLET FORMS ON FRACTALS

Masanori Hino and Takashi Kumagai

We consider a trace theorem for self-similar Dirichlet forms on self- 
similar
sets to self-similar subsets. In particular, we characterize the  
trace of the
domains of Dirichlet forms on the Sierpinski gaskets and the  
Sierpinski carpets
to their boundaries, where boundaries mean the triangles and  
rectangles which
confine gaskets and carpets. As an application, we construct diffusion
processes on a collection of fractals called fractal fields, which  
behave as
the appropriate fractal diffusion within each fractal component of  
the field.


http://front.math.ucdavis.edu/math.PR/0510553

---------------------------------------------------------------

3737. THE CRITICAL BRANCHING MARKOV CHAIN IS TRANSIENT

Nina Gantert and Sebastian Mueller

We investigate recurrence and transience of Branching Markov Chains  
(BMC) in
discrete time. Branching Markov Chains are clouds of particles which  
move
(according to an irreducible underlying Markov Chain) and produce  
offspring
independently. The offspring distribution can depend on the location  
of the
particle. If the offspring distribution is constant for all  
locations, these
are Tree-Indexed Markov chains in the sense of \cite{benjamini94}.  
Starting
with one particle at location $x$, we denote by $\alpha(x)$ the  
probability
that $x$ is visited infinitely often by the cloud. Due to the  
irreducibility of
the underlying Markov Chain, there are three regimes: either $\alpha 
(x) = 0$
for all $x$ (transient regime), or $0 < \alpha(x) < 1$ for all $x$  
(weakly
recurrent regime) or $\alpha(x) = 1$ for all $x$ (strongly recurrent  
regime).
We give classification results, including a sufficient condition for  
transience
in the general case.
  If the mean of the offspring distribution is constant, we give a  
criterion for
transience involving the spectral radius of the underlying Markov  
Chain and the
mean of the offspring distribution.


http://front.math.ucdavis.edu/math.PR/0510556

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3738. WINNING RATE IN THE FULL-INFORMATION BEST CHOICE PROBLEM

Alexander Gnedin and Denis Miretskiy

Following a long-standing suggestion by Gilbert and Mosteller, we  
derive an
explicit formula for the asymptotic winning rate in the full-information
problem of the best choice.


http://front.math.ucdavis.edu/math.PR/0510568

---------------------------------------------------------------

3739. LIMITING LAWS ASSOCIATED WITH BROWNIAN MOTION PERTURBED BY ITS  
MAXIMUM,  MINMUM AND LOCAL TIME II

Bernard Roynette (IEC) and  Pierre Vallois (IEC) and  Marc Yor (PMA)

We obtain probability measures on the canonical space penalizing the  
Wiener
measure by a function of its maximum (resp. minimum, local time). We  
study the
law of the canonical process under these new probability measures.


http://front.math.ucdavis.edu/math.PR/0510575

---------------------------------------------------------------

3740. A NOTE ON THE HARRIS-KESTEN THEOREM

Bela Bollobas and Ronald Meester and Oliver Riordan

Recently, a short proof of the Harris-Kesten result that the critical
probability for bond percolation in the planar square lattice is 1/2  
was given,
using a sharp threshold result of Friedgut and Kalai. Here we point  
out that a
key part of this proof may be replaced by an argument of Russo from  
1982, using
his approximate zero-one law in place of the Friedgut-Kalai result.  
Russo's
paper gave a new proof of the Harris-Kesten Theorem that seems to  
have received
little attention.


http://front.math.ucdavis.edu/math.PR/0509131

---------------------------------------------------------------

3741. MULTIVARIATE NORMAL APPROXIMATIONS BY STEIN'S METHOD AND SIZE  
BIAS  COUPLINGS

Larry Goldstein and  Yosef Rinott

Stein's method is used to obtain two theorems on multivariate normal
approximation. Our main theorem, Theorem 1.2, provides a bound on the  
distance
to normality for any nonnegative random vector. Theorem 1.2 requires
multivariate size bias coupling, which we discuss in studying the  
approximation
of distributions of sums of dependent random vectors. In the  
univariate case,
we briefly illustrate this approach for certain sums of nonlinear  
functions of
multivariate normal variables. As a second illustration, we show that  
the
multivariate distribution counting the number of vertices with given  
degrees in
certain random graphs is asymptotically multivariate normal and  
obtain a bound
on the rate of convergence. Both examples demonstrate that this  
approach may be
suitable for situations involving non-local dependence. We also  
present Theorem
1.4 for sums of vectors having a local type of dependence. We apply this
theorem to obtain a multivariate normal approximation for the  
distribution of
the random $p$-vector which counts the number of edges in a fixed  
graph both of
whose vertices have the same given color when each vertex is colored  
by one of
$p$ colors independently. All normal approximation results presented  
here do
not require an ordering of the summands related to the dependence  
structure.
This is in contrast to hypotheses of classical central limit theorems  
and
examples, which involve e.g., martingale, Markov chain, or various  
mixing
assumptions.


http://front.math.ucdavis.edu/math.PR/0510586

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3742. AN UNEXPECTED CONNECTION BETWEEN BRANCHING PROCESSES AND  
OPTIMAL  STOPPING

David Assaf and  Larry Goldstein and  and Ester Samuel-Cahn

A curious connection exists between the theory of optimal stopping for
independent random variables, and branching processes. In particular,  
for the
branching process $Z_n$ with offspring distribution $Y$, there exists  
a random
variable $X$ such that the probability $P(Z_n=0)$ of extinction of  
the $n$th
generation in the branching process equals the value obtained by  
optimally
stopping the sequence $X_1,...,X_n$, where these variables are i.i.d
distributed as $X$. Generalizations to the inhomogeneous and infinite  
horizon
cases are also considered. This correspondence furnishes a simple  
`stopping
rule' method for computing various characteristics of branching  
processes,
including rates of convergence of the $n^{th}$ generation's extinction
probability to the eventual extinction probability, for the  
supercritical,
critical and subcritical Galton-Watson process. Examples, bounds,  
further
generalizations and a connection to classical prophet inequalities are
presented. Throughout, the aim is to show how this unexpected  
connection can be
used to translate methods from one area of applied probability to  
another,
rather than to provide the most general results.


http://front.math.ucdavis.edu/math.PR/0510587

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3743. OVERCROWDING ESTIMATES FOR ZEROES OF PLANAR AND HYPERBOLIC  
GAUSSIAN  ANALYTIC FUNCTIONS

Manjunath Krishnapur

We consider the point process of zeroes of certain Gaussian analytic
functions and find the asymptotics for the probability that there are  
more than
m points of the process in a fixed disk of radius r, as m-->infinity.  
For the
Planar Gaussian analytic function, sum_n a_n z^n/sqrt(n!), we show  
that this
probability is asymptotic to exp(-0.5 m^2 log(m)). For the Hyperbolic  
Gaussian
analytic functions, sum_n sqrt({-rho choose n}) a_n z^n, rho>0, we  
show that
this probability decays like exp(-cm^2).
  In the planar case, we also consider the problem posed by Mikhail  
Sodin on
moderate and very large deviations in a disk of radius r as r -->  
infinity. We
partly solve the problem by showing that there is a qualitative  
change in the
asymptotics of the probability as we move from the large deviation  
regime to
the moderate.


http://front.math.ucdavis.edu/math.PR/0510588

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3744. A LARGE DEVIATION APPROACH TO SOME TRANSPORTATION COST  
INEQUALITIES

Nathael Gozlan (MODAL'X) and  Christian L\'{e}onard (MODAL'X and  CMAP)

New transportation cost inequalities are derived by means of  
elementary large
deviation reasonings. Their dual characterization is proved; this  
provides an
extension of a well-known result of S. Bobkov and F. G\"{o}tze. Their
tensorization properties are investigated. Sufficient conditions (and  
necessary
conditions too) for these inequalities are stated in terms of the  
integrability
of the reference measure. Applying these results leads to new deviation
results: concentration of measure and deviations of empirical processes.


http://front.math.ucdavis.edu/math.PR/0510601

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3745. MONTE CARLO COMPARISONS OF THE SELF-AVOIDING WALK AND SLE AS   
PARAMETERIZED CURVES

Tom Kennedy

The scaling limit of the two-dimensional self-avoiding walk (SAW) is  
believed
to be given by the Schramm-Loewner evolution (SLE) with the parameter  
kappa
equal to 8/3. The scaling limit of the SAW has a natural  
parameterization and
SLE has a standard parameterization using the half-plane capacity.  
These two
parameterizations do not correspond with one another. To make the  
scaling limit
of the SAW and SLE agree as parameterized curves, we must  
reparameterize one of
them. We present Monte Carlo results that show that if we  
reparameterize the
SAW using the half-plane capacity, then it agrees well with SLE with its
standard parameterization. We then consider how to reparameterize SLE  
to make
it agree with the SAW with its natural parameterization. We argue  
using Monte
Carlo results that the so-called p-variation of the SLE curve with  
p=1/nu=4/3
provides a parameterization that corresponds to the natural  
parameterization of
the SAW.


http://front.math.ucdavis.edu/math.PR/0510604

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3746. ASYMPTOTICS FOR FIRST-PASSAGE TIMES ON DELAUNAY TRIANGULATIONS

Leandro P. R. Pimentel

In this paper we study first-passge percolation models on Delaunay
triangulations. We show a sufficient condition to ensure that the  
asymptotic
value of the rescaled first-passage time, called the time constant,  
is strictly
positive and derive some upper bounds for fluctuations. Our proofs  
are based on
renormalization ideas and on the method of bounded increments.


http://front.math.ucdavis.edu/math.PR/0510605

---------------------------------------------------------------

3747. STEIN'S METHOD AND THE ZERO BIAS TRANSFORMATION WITH  
APPLICATION TO  SIMPLE RANDOM SAMPLING

Larry Goldstein and  Gesine Reinert

Let $W$ be a random variable with mean zero and variance $\sigma^2$. The
distribution of a variate $W^*$, satisfying $EWf(W)=\sigma ^2 Ef'(W^*) 
$ for
smooth functions $f$, exists uniquely and defines the zero bias  
transformation
on the distribution of $W$. The zero bias transformation shares many
interesting properties with the well known size bias transformation for
non-negative variables, but is applied to variables taking on both  
positive and
negative values. The transformation can also be defined on more  
general random
objects. The relation between the transformation and the expression
$wf'(w)-\sigma^2 f''(w)$ which appears in the Stein equation  
characterizing the
mean zero, variance $\sigma ^2$ normal $\sigma Z$ can be used to  
obtain bounds
on the difference $E\{h(W/\sigma)-h(Z)\}$ for smooth functions $h$ by
constructing the pair $(W,W^*)$ jointly on the same space. When $W$  
is a sum of
$n$ not necessarily independent variates, under certain conditions which
include a vanishing third moment, bounds on this difference of the  
order $1/n$
for classes of smooth functions $h$ may be obtained. The technique is
illustrated by an application to simple random sampling.


http://front.math.ucdavis.edu/math.PR/0510619

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3748. THE SCALING LIMIT GEOMETRY OF NEAR-CRITICAL 2D PERCOLATION

F. Camia and  L. R. G. Fontes and  C. M. Newman

We analyze the geometry of scaling limits of near-critical 2D  
percolation,
i.e., for $p=p_c+\lambda\delta^{1/\nu}$, with $\nu=4/3$, as the  
lattice spacing
$\delta \to 0$. Our proposed framework extends previous analyses for  
$p=p_c$,
based on $SLE_6$. It combines the continuum nonsimple loop process  
describing
the full scaling limit at criticality with a Poissonian process for  
marking
double (touching) points of that (critical) loop process. The double  
points are
exactly the continuum limits of "macroscopically pivotal" lattice  
sites and the
marked ones are those that actually change state as $\lambda$ varies.  
This
structure is rich enough to yield a one-parameter family of near- 
critical loop
processes and their associated connectivity probabilities as well as  
related
processes describing, e.g., the scaling limit of 2D minimal spanning  
trees.


http://front.math.ucdavis.edu/cond-mat/0510740

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3749. DYNAMIC STATE TAMENESS

Jaime A. Londo\~no

An extension of the idea of state tameness is presented in a dynamic
framework. The proposed model for financial markets is rich enough to  
provide
analytical tools that are mostly obtained in models that arise as the  
solution
of SDEs with deterministic coefficients. In the presented model the
augmentation by a shadow stock of the price evolution has a Markovian
character. As in a previous paper, the results obtained on valuation of
European contingent claims and American contingent claims do not  
require the
full range of the volatility matrix. Under some additional continuity
conditions, the conceptual framework provided by the model makes it  
possible to
regard the valuation of financial instruments of the European type as a
particular case of valuation of instruments of American type. This  
provides a
unifying framework for the problem of valuation of financial  
instruments.


http://front.math.ucdavis.edu/math.PR/0509139

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3750. SPLITTING OF LIFTINGS IN PRODUCTS OF PROBABILITY SPACES

W. Strauss and  N. D. Macheras and K. Musial

We prove that if (X,\mathfrakA,P) is an arbitrary probability space with
countably generated \sigma-algebra \mathfrakA, (Y,\mathfrakB,Q) is an  
arbitrary
complete probability space with a lifting \rho and \hat R is a complete
probability measure on \mathfrakA \hat \otimes_R \mathfrakB  
determined by a
regular conditional probability {S_y:y\in Y} on \mathfrakA with  
respect to
\mathfrakB, then there exist a lifting \pi on (X\times Y,\mathfrakA \hat
\otimes_R \mathfrakB,\hat R) and liftings \sigma_y on (X,\hat  
\mathfrakA_y,\hat
S_y), y\in Y, such that, for every E\in\mathfrakA \hat \otimes_R  
\mathfrakB and
every y\in Y, [\pi(E)]^y=\sigma_y\bigl([\pi(E)]^y\bigr). Assuming the  
absolute
continuity of R with respect to P\otimes Q, we prove the existence of  
a regular
conditional probability {T_y:y\in Y} and liftings \varpi on (X\times
Y,\mathfrakA \hat \otimes_R \mathfrakB,\hat R), \rho' on (Y, 
\mathfrakB,\hat Q)
and \sigma_y on (X,\hat \mathfrakA_y,\hat S_y), y\in Y, such that,  
for every
E\in\mathfrakA \hat \otimes_R \mathfrakB and every y\in Y,
[\varpi(E)]^y=\sigma_y\bigl([\varpi(E)]^y\bigr) and \varpi(A\times
B)=\bigcup_{y\in\rho'(B)}\sigma_y(A)\times{y}\qquadif A\times
B\in\mathfrakA\times\mathfrakB. Both results are generalizations of  
Musia\l,
Strauss and Macheras [Fund. Math. 166 (2000) 281-303] to the case of  
measures
which are not necessarily products of marginal measures. We prove  
also that
liftings obtained in this paper always convert \hat R-measurable  
stochastic
processes into their \hat R-measurable modifications.


http://front.math.ucdavis.edu/math.PR/0509010

---------------------------------------------------------------

3751. STATIONARY SOLUTIONS OF STOCHASTIC DIFFERENTIAL EQUATION WITH  
MEMORY AND  STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS

Yuri Bakhtin and Jonathan C. Mattingly

We explore Ito stochastic differential equations where the drift term
possibly depends on the infinite past. Assuming the existence of a  
Lyapunov
function, we prove the existence of a stationary solution assuming  
only minimal
continuity of the coefficients. Uniqueness of the stationary solution  
is proven
if the dependence on the past decays sufficiently fast. The results  
of this
paper are then applied to stochastically forced dissipative partial
differential equations such as the stochastic Navier-Stokes equation and
stochastic Ginsburg-Landau equation.


http://front.math.ucdavis.edu/math.PR/0509166

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3752. BENFORD'S LAW FOR THE $3X+1$ FUNCTION

Jeffrey C. Lagarias and K. Soundararajan

We show that for most choices of an initial seed $x_0$, the sequence  
of the
first $N$ iterates of $x_0$ under the $3x+1$ map approximately satisfies
Benford's law.


http://front.math.ucdavis.edu/math.NT/0509175

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3753. APPENDIX TO THE PAPER "RANDOM WALKS ON FREE PRODUCTS OF CYCLIC  
GROUPS"

Jean Mairesse and Fr\'ed\'eric Math\'eus

This paper is an appendix to the paper "Random walks on free products of
cyclic groups" by J.Mairesse and F.Math\'eus. It contains the details  
of the
computations and the proofs of the results concerning the examples  
treated
there.


http://front.math.ucdavis.edu/math.PR/0509208

---------------------------------------------------------------

3754. RANDOM WALKS ON FREE PRODUCTS OF CYCLIC GROUPS

Jean Mairesse and Fr\'ed\'eric Math'eus

Let G be a free product of a finite family of finite groups, with the  
set of
generators being formed by the union of the finite groups. We consider a
transient nearest-neighbour random walk on G. We give a new proof of  
the fact
that the harmonic measure is a special Markovian measure entirely  
determined by
a finite set of polynomial equations. We show that in several simple  
cases of
interest, the polynomial equations can be explicitely solved, to get  
closed
form formulas for the drift. The examples considered are the modular  
group
Z/2Z*Z/3Z, Z/3Z*Z/3Z, Z/kZ*Z/kZ, and the Hecke groups Z/2Z*Z/kZ. We  
also use
these various examples to study Vershik's notion of extremal  
generators, which
is based on the relation between the drift, the entropy, and the  
volume of the
group.


http://front.math.ucdavis.edu/math.PR/0509211

---------------------------------------------------------------

3755. STOCHASTIC VOLTERRA EQUATIONS OF NONSCALAR TYPE

Anna Karczewska

In the paper stochastic Volterra equations of nonscalar type are studied
using resolvent approach. The aim of this note is to provide some  
results on
stochastic convolution and integral mild solutions to those Volterra  
equations.
The motivation of the paper comes from a model of aging viscoelastic  
materials.


http://front.math.ucdavis.edu/math.PR/0509012

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3756. PERCOLATION, PERIMETRY, PLANARITY

Gady Kozma

Let G be a planar graph with polynomial growth and isoperimetric  
dimension
bigger than 1. Then the critical p for Bernoulli percolation on G  
satisfies
p<1.


http://front.math.ucdavis.edu/math.PR/0509235

---------------------------------------------------------------

3757. ON THE EXPANSION OF THE GIANT COMPONENT IN PERCOLATED (N,D, 
\LAMBDA)  GRAPHS

Eran Ofek

Let d be a sufficiently large constant. A (n,d,c sqrt{d}) graph G is a d
regular graph over n vertices whose second largest eigenvalue (in  
absolute
value) is at most c sqrt{d}. For any 0 < p < 1, G_p is the graph  
induced by
retaining each edge of G with probability p. We show that for any p >
5c/sqrt{d} the graph G_p almost surely contains a unique giant  
component (a
connected component with linear number vertices). We further show  
that the
giant component of G_p almost surely has an edge expansion of at  
least 1/(log_2
n).


http://front.math.ucdavis.edu/math.PR/0509253

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3758. CARNE-VAROPOULOS BOUNDS FOR CENTERED RANDOM WALKS

Pierre Mathieu

We extend the Carne-Varopoulos upper bound on the probability  
transitions of
a Markov chain to a certain class of non-reversible processes by  
introducing
the definition of a `centering measure'. In the case of random walks  
on a
group, we study the connections between different notions of centering.


http://front.math.ucdavis.edu/math.PR/0509257

---------------------------------------------------------------

3759. DETERMINISTIC MODAL BAYESIAN LOGIC: DERIVE THE BAYESIAN WITHIN  
THE MODAL  LOGIC T

Frederic Dambreville (DGA/CEP/GIP/SRO)

In this paper a conditional logic is defined and studied. This  
conditional
logic, DmBL, is constructed as close as possible to the Bayesian and is
unrestricted, that is one is able to use any operator without  
restriction. A
notion of logical independence is also defined within the logic  
itself. This
logic is shown to be non trivial and is not reduced to classical  
propositions.
A model is constructed for the logic. Completeness results are  
proved. It is
shown that any unconditioned probability can be extended to the whole  
logic
DmBL. The Bayesian is then recovered from the probabilistic DmBL. At  
last, it
is shown why DmBL is compliant with Lewis triviality.


http://front.math.ucdavis.edu/math.LO/0509248

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3760. ERROR ANALYSIS OF COARSE-GRAINED KINETIC MONTE CARLO METHOD

Markos A Katsoulakis and  Petr Plechac and  Alexandros Sopasakis

In this paper we investigate the approximation properties of the
coarse-graining procedure applied to kinetic Monte Carlo simulations  
of lattice
stochastic dynamics. We provide both analytical and numerical  
evidence that the
hierarchy of the coarse models is built in a systematic way that  
allows for
error control in both transient and long-time simulations. We  
demonstrate that
the numerical accuracy of the CGMC algorithm as an approximation of  
stochastic
lattice spin flip dynamics is of order two in terms of the coarse- 
graining
ratio and that the natural small parameter is the coarse-graining  
ratio over
the range of particle/particle interactions. The error estimate is  
shown to
hold in the weak convergence sense. We employ the derived analytical  
results to
guide CGMC algorithms and we demonstrate a CPU speed-up in demanding
computational regimes that involve nucleation, phase transitions and
metastability.


http://front.math.ucdavis.edu/math.NA/0509228

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3761. CONDITIONED SQUARE FUNCTIONS FOR NON-COMMUTATIVE MARTINGALES

Narcisse Randrianantoanina

We prove a weak-type (1,1) inequality involving conditioned square  
functions
of martingales in non-commutative $L^p$-spaces associated with finite  
von
Neumann algebras. As application, we determine the optimal orders for  
the best
constants in the non-commutative Burkholder/Rosenthal inequalities  
from Ann.
Proba. 31 (2003), 948-995. We also discuss BMO-norms of sums of non- 
commuting
order independent operators.


http://front.math.ucdavis.edu/math.OA/0509226

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3762. CALCULATION OF GREEKS FOR JUMP-DIFFUSIONS

Barbara Forster and  Eva Luetkebohmert and  Josef Teichmann

Calculation of Greeks by Malliavin weights has proved to be a  
numerically
satisfactory procedure for usual Ito-diffusions. In this article we  
prove
existence of Malliavin weights for jump diffusions under H\"{o}rmander
conditions and hypotheses on the invertibility of the linkage  
operators. The
main result -- in the hypo-ellitpic case -- is the invertibility of the
covariance matrix, which enables -- by usual methods -- the  
construction of the
relevant Malliavin weights. The message is that in fairly general
jump-diffusion cases one should proceed such as in pure diffusion  
cases. In
contrast to Davis et al. we do not need any separability assumptions.


http://front.math.ucdavis.edu/math.PR/0509016

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3763. BROWNIAN MOTION ON TIME SCALES, BASIC HYPERGEOMETRIC FUNCTIONS,  
AND SOME  CONTINUED FRACTIONS OF RAMANUJAN

Shankar Bhamidi and Steven N. Evans and Ron Peled and Peter Ralph

Motivated by L\'evy's characterization of Brownian motion on the  
line, we
propose an analogue of Brownian motion that has as its state space an  
arbitrary
unbounded closed subset of the line: such a process will be a Feller- 
Dynkin
process that is a martingale, has the identity function as its quadratic
variation process, and is ``continuous'' in the sense that its sample  
paths
don't skip over points. We show that there is a unique such process  
and find
its generator. We then consider the special case where the state  
space is the
self-similar set $\{\pm q^k : k \in \Z\} \cup \{0\}$ for some $q>1$.  
Using the
scaling properties of the process, we represent the Laplace  
transforms of
various hitting times as certain continued fractions that appear in  
Ramanujan's
``lost'' notebook and evaluate these continued fractions in terms of
$q$-analogues of classical hypergeometric functions. The process has  
0 as a
regular instantaneous point, and hence its sample paths can be  
decomposed into
a Poisson process of excursions from 0 using the associated  
continuous local
time. We find the entrance laws of the corresponding It\^o excursion  
measure
and the Laplace exponent of the inverse local time -- both again in  
terms of
basic hypergeometric functions -- and hence obtain explicit formulae  
for the
resolvent of the process.


http://front.math.ucdavis.edu/math.PR/0509270

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3764. SOLUTIONS OF MAX-PLUS LINEAR EQUATIONS AND LARGE DEVIATIONS

Marianne Akian and  Stephane Gaubert and Vassili Kolokoltsov

We generalise the Gartner-Ellis theorem of large deviations theory. Our
results allow us to derive large deviation type results in stochastic  
optimal
control from the convergence of generalised logarithmic moment  
generating
functions. They rely on the characterisation of the uniqueness of the  
solutions
of max-plus linear equations. We give an illustration for a simple  
investment
model, in which logarithmic moment generating functions represent
risk-sensitive values.


http://front.math.ucdavis.edu/math.PR/0509279

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3765. SECOND ORDER BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS AND  
FULLY  NON-LINEAR PARABOLIC PDES

Patrick Cheridito and  H. Mete Soner and  Nizar Touzi and  Nicolas  
Victoir

We introduce a class of second order backward stochastic differential
equations and show relations to fully non-linear parabolic PDEs. In  
particular,
we provide a stochastic representation result for solutions of such  
PDEs and
discuss Monte Carlo methods for their numerical treatment.


http://front.math.ucdavis.edu/math.PR/0509295

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3766. DISAGGREGATION OF LONG MEMORY PROCESSES ON C^{\INFTY} CLASS

Didier Dacunha-Castelle and  Lisandro Ferm\'{\i}n

We prove that a large set of long memory (LM) processes (including  
classical
LM processes and all processes whose spectral densities have a  
countable number
of singularities controlled by exponential functions) are obtained by an
aggregation procedure involving short memory (SM) processes whose  
spectral
densities are infinitely differentiable (C^{infty}). We show that the  
C^{infty}
class of spectral densities is the optimal class to get a general  
result for
disaggregation of LM processes in SM processes, in the sense that the  
result
given in C^{infty} class cannot be improved taking for instance analytic
functions instead of indefinitely derivable functions.


http://front.math.ucdavis.edu/math.PR/0509308

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3767. LARGE DEVIATIONS ASYMPTOTICS AND THE SPECTRAL THEORY OF  
MULTIPLICATIVELY  REGULAR MARKOV PROCESSES

Ioannis Kontoyiannis (Athens U Econ & Business) and  S.P. Meyn (Univ  
Ill.  Urbana-Champaign)

We continue the investigation of the spectral theory and exponential
asymptotics of Markov processes, following Kontoyiannis and Meyn  
(2003). We
introduce a new family of nonlinear Lyapunov drift criteria,  
characterizing
distinct subclasses of geometrically ergodic Markov processes in  
terms of
inequalities for the nonlinear generator. We concentrate on the class of
"multiplicatively regular" Markov processes, characterized via  
conditions
similar to (but weaker than) those of Donsker-Varadhan. For any such  
process
{Phi(t)} with transition kernel P on a general state space, the  
following are
obtained. 1. SPECTRAL THEORY: For a large class of functionals F, the  
kernel
Phat(x,dy) = e^{F(x)}P(x,dy) has a discrete spectrum in an appropriately
defined Banach space. There exists a "maximal" solution to the  
"multiplicative
Poisson equation," defined as the eigenvalue problem for Phat.  
Regularity
properties are established for \Lambda(F) = \log(\lambda), where  
\lambda is the
maximal eigenvalue, and for its convex dual. 2. MULTIPLICATIVE MEAN  
ERGODIC
THEOREM: The normalized mean E_x[\exp(S_t)] of the exponential of the  
partial
sums {S_t} of the process with respect to any one of the above  
functionals F,
converges to the maximal eigenfunction. 3. MULTIPLICATIVE REGULARITY:  
The drift
criterion under which our results are derived is equivalent to the  
existence of
regeneration times with finite exponential moments for {S_t}. 4. LARGE
DEVIATIONS: The sequence of empirical measures of {Phi(t)} satisfies  
an LDP in
a topology finer than the \tau-topology. The rate function is  
\Lambda^* and it
coincides with the Donsker-Varadhan rate function. 5. EXACTR LARGE  
DEVIATIONS:
The partial sums {S_t} satisfy an exact LD expansion, analogous to that
obtained for independent random variables.


http://front.math.ucdavis.edu/math.PR/0509310

---------------------------------------------------------------

3768. PATHWISE ASYMPTOTIC BEHAVIOR OF RANDOM DETERMINANTS IN THE  
UNIFORM GRAM  AND WISHART ENSEMBLES

Alain Rouault

This paper concentrates on asymptotic properties of determinants of some
random symmetric matrices. If B_{n,r} is a n x r rectangular matrix and
B_{n,r}' its transpose, we study det (B_{n,r}'B_{n,r}) when n,r tends to
infinity with r/n \to c\in (0,1). The r column vectors of B_{n,r} are  
chosen
independently, with common distribution \nu_n. The Wishart ensemble  
corresponds
to \nu_n = {\cal N}(0, I_n), the standard normal distribution. We  
call uniform
Gram ensemble the ensemble corresponding to \nu_n = \sigma_n, the  
uniform
distribution on the unit sphere `S_{n-1}. In the Wishart ensemble, a  
well known
Bartlett's theorem decomposes the above determinant into a product of
chi-square variables. The same holds in the uniform Gram ensemble.  
This allows
us to study the process \{\frac{1}{n}\log \det\big(B_{n,\lfloor
nt\rfloor}'B_{n,\lfloor nt\rfloor}\big), t \in [0,1]\} and its  
asymptotic
behavior as n\to \infty: a.s. convergence, fluctuations, large  
deviations. We
connect the results for marginals (fixed t) with those obtained by  
the spectral
method.


http://front.math.ucdavis.edu/math.PR/0509021

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3769. STATIONARY PROCESSES WHOSE FILTRATIONS ARE STANDARD

X. Bressaud and  A. Maass and  S. Martinez and  J. San Martin

We study the standard property of the natural filtration associated  
to a 0-1
valued stationary process. In our main result we show that if the  
process has
summable memory decay, then the associated filtration is standard. We  
prove it
by coupling techniques. For a process whose associated filtration is  
standard
we construct a product type filtration extending it, based upon the  
usual
couplings and the Vershik's criterion for standardness.


http://front.math.ucdavis.edu/math.PR/0509317

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3770. THE DENSITY OF THE ISE AND LOCAL LIMIT LAWS FOR EMBEDDED TREES

Mireille Bousquet-M\'{e}lou (LaBRI) and  Svante Janson

It has been known for a few years that the occupation measure of several
models of embedded trees converges, after a suitable normalization,  
to the
random measure called ISE (Integrated SuperBrownian Excursion). Here,  
we prove
a local version of this result: ISE has a (random) H\"{o}lder continuous
density, and the vertical profile of embedded trees converges to this  
density,
at least for some such trees. As a consequence, we derive a formula  
for the
distribution of the density of ISE at a given point. This follows  
from earlier
results by Bousquet-M\'{e}lou on convergence of the vertical profile  
at a fixed
point. We also provide a recurrence relation defining the moments of the
(random) moments of ISE.


http://front.math.ucdavis.edu/math.PR/0509322

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3771. NORM DISCONTINUITY AND SPECTRAL PROPERTIES OF ORNSTEIN- 
UHLENBECK  SEMIGROUPS

Jan van Neerven and  Enrico Priola

Let $E$ be a real Banach space. We study the Ornstein-Uhlenbeck  
semigroup
$P(t)$ associated with the Ornstein-Uhlenbeck operator $$ Lf(x) =  
\frac12 {\rm
Tr} Q D^2 f(x) + <Ax, Df(x)>.$$ Here $Q$ is a positive symmetric  
operator from
$E^*$ to $E$ and $A$ is the generator of a $C_0$-semigroup $S(t)$ on  
$E$. Under
the assumption that $P$ admits an invariant measure $\mu$ we prove  
that if $S$
is eventually compact and the spectrum of its generator is nonempty,  
then $$\n
P(t)-P(s)\n_{L^1(E,\mu)} = 2$$ for all $t,s\ge 0$ with $t\not=s$.  
This result
is new even when $E = \R^n$. We also study the behaviour of $P$ in  
the space
$BUC(E)$. We show that if $A\not=0$ there exists $t_0>0$ such that $$\n
P(t)-P(s)\n_{BUC(E)} = 2$$ for all $0\le t,s\le t_0$ with $t\not=s$.  
Moreover,
under a nondegeneracy assumption or a strong Feller assumption, the  
following
dichotomy holds: either $$ \n P(t)- P(s)\n_{BUC(E)} = 2$$ for all $t,s 
\ge 0$, \
$t\not=s$, or $S$ is the direct sum of a nilpotent semigroup and a
finite-dimensional periodic semigroup. Finally we investigate the  
spectrum of
$L$ in the spaces $L^1(E,\mu)$ and $BUC(E)$.


http://front.math.ucdavis.edu/math.FA/0509309

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3772. APPROXIMATION OF ROUGH PATHS OF FRACTIONAL BROWNIAN MOTION

Annie Millet (PMA) and  Marta Sanz-Sol\'{e}

We consider a geometric rough path associated with a fractional Brownian
motion with Hurst parameter $H\in]{1/4}, {1/2}[$. We give an  
approximation
result in a modulus type distance, up to the second order, by means of a
sequence of rough paths lying above elements of the reproducing  
kernel Hilbert
space.


http://front.math.ucdavis.edu/math.PR/0509353

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3773. GAME THEORETIC DERIVATION OF DISCRETE DISTRIBUTIONS AND  
DISCRETE PRICING  FORMULAS

Akimichi Takemura and Taiji Suzuki

In this expository paper we illustrate the generality of game theoretic
probability protocols of Shafer and Vovk (2001) in finite-horizon  
discrete
games. By restricting ourselves to finite-horizon discrete games, we can
explicitly describe how discrete distributions with finite support  
and the
discrete pricing formulas, such as the Cox-Ross-Rubinstein formula, are
naturally derived from game-theoretic probability protocols.  
Corresponding to
any discrete distribution with finite support, we construct a finite- 
horizon
discrete game, a replicating strategy of Skeptic, and a neutral  
forecasting
strategy of Forecaster, such that the discrete distribution is  
derived from the
game. Construction of a replicating strategy is the same as in the  
standard
arbitrage arguments of pricing European options in the binomial tree  
models.
However the game theoretic framework is advantageous because no a priori
probabilistic assumption is needed.


http://front.math.ucdavis.edu/math.PR/0509367

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3774. STEPPING-STONE MODEL WITH CIRCULAR BROWNIAN MIGRATION

Xiaowen Zhou

In this paper we consider a stepping-stone model on a circle with  
circular
Brownian migration. We first point out a connection between Arratia  
flow and
the marginal distribution of this model. We then give a new  
representation for
the stepping-stone model using Arratia flow and circular coalescing  
Brownian
motion. Such a representation enables us to carry out some explicit
computation. In particular, we find the Laplace transform for the  
time when
there is only a single type left across the circle.


http://front.math.ucdavis.edu/math.PR/0509383

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3775. THE ISOPERIMETRIC CONSTANT OF THE RANDOM GRAPH PROCESS

Itai Benjamini and  Simi Haber and  Michael Krivelevich and  Eyal  
Lubetzky

The isoperimetric constant of a graph $G$ on $n$ vertices, $i(G)$, is  
the
minimum of $\frac{|\partial S|}{|S|}$, taken over all nonempty subsets
$S\subset V(G)$ of size at most $n/2$, where $\partial S$ denotes the  
set of
edges with precisely one end in $S$. A random graph process on $n$  
vertices,
$\widetilde{G}(t)$, is a sequence of $\binom{n}{2}$ graphs, where
$\widetilde{G}(0)$ is the edgeless graph on $n$ vertices, and
$\widetilde{G}(t)$ is the result of adding an edge to $\widetilde{G} 
(t-1)$,
uniformly distributed over all the missing edges. We show that in  
almost every
graph process $i(\widetilde{G}(t))$ equals the minimal degree of
$\widetilde{G}(t)$ as long as the minimal degree is $o(\log n)$.  
Furthermore,
we show that this result is essentially best possible, by  
demonstrating that
along the period in which the minimum degree is typically $\Theta 
(\log n)$, the
ratio between the isoperimetric constant and the minimum degree falls  
from 1 to
1/2, its final value.


http://front.math.ucdavis.edu/math.PR/0509022

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3776. SPECTRAL ANALYSIS OF SINAI'S WALK FOR SMALL EIGENVALUES

A. Bovier and  A. Faggionato

Sinai's walk can be thought of as a random walk on the set of interger
numbers with random potential V, with V weakly converging under  
diffusive
rescaling to a two-sided Brownian motion. We consider here the  
generator L_N of
Sinai's walk on [-N,N] with Dirichlet conditions on -N,N. By means of  
potential
theory, for each h>0 we show the relation between the spectral  
properties of
L_N for eigenvalues of order o(exp{-h N^{1/2}}) and the distribution  
of the
h-extrema of the rescaled potential V_N(x)=V(Nx)/N^{1/2} defined on  
[-1,1].
Information about the h-extrema of V_N is derived from a result of  
Neveu and
Pitman concerning the statistics of h-extrema of Brownian motion. As  
first
application of our results, we give a proof of a refined version of  
Sinai's
localization theorem.


http://front.math.ucdavis.edu/math.PR/0509385

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3777. EUCLIDEAN GIBBS MEASURES OF QUANTUM ANHARMONIC CRYSTALS

Yuri Kozitsky and Tatiana Pasurek

A lattice system of interacting temperature loops, which is used in the
Euclidean approach to describe equilibrium thermodynamic properties  
of an
infinite system of interacting quantum particles performing anharmonic
oscillations (quantum anharmonic crystal), is considered. For this  
system, it
is proven that: (a) the set of tempered Gibbs measures is non-void  
and weakly
compact; (b) every Gibbs measure obeys an exponential integrability  
estimate,
the same for all such measures; (c) every Gibbs measure has a  
Lebowitz-Presutti
type support; (d) the set of all Gibbs measures is a singleton at high
temperatures. In the case of attractive interaction and one-dimensional
oscillations we prove that at low temperatures the system undergoes a  
phase
transition. The uniqueness of Gibbs measures due to strong quantum  
effects
(strong diffusivity) and at a nonzero external field are also proven  
in this
case. Thereby, a complete description of the properties of the set of  
all Gibbs
measures has been done, which essentially extends and refines the  
results
obtained so far for models of this type.


http://front.math.ucdavis.edu/math-ph/0509036

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3778. NONEXISTENCE OF SOLUTIONS IN $(0,1)$ FOR K-P-P-TYPE EQUATIONS  
FOR ALL  $D\GE 1$

J. Englander and P. L. Simon

Consider the KPP-type equation of the form $\Delta u+f(u)=0$, where  
$f:[0,1]
\to \mathbb R_{+}$ is a concave function. We prove for arbitrary  
dimensions
that there is no solution bounded in $(0,1)$. The significance of  
this result
from the point of view of probability theory is also discussed.


http://front.math.ucdavis.edu/math.AP/0509384

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3779. PROBABILISTIC EXTENSIONS OF THE ERD\H OS-KO-RADO PROPERTY

Anna Celaya and  Anant P. Godbole and  Mandy Rae Schleifer

The classical Erd\H os-Ko-Rado (EKR) Theorem states that if we choose a
family of subsets, each of size (k), from a fixed set of size (n (n >  
2k)),
then the largest possible pairwise intersecting family has size (t = 
{n-1\choose
k-1}). We consider the probability that a randomly selected family of  
size
(t=t_n) has the EKR property (pairwise nonempty intersection) as $n$ and
$k=k_n$ tend to infinity, the latter at a specific rate. As $t$ gets  
large, the
EKR property is less likely to occur, while as $t$ gets smaller, the EKR
property is satisfied with high probability. We derive the threshold  
value for
$t$ using Janson's inequality. Using the Stein-Chen method we show  
that the
distribution of $X_0$, defined as the number of disjoint pairs of  
subsets in
our family, can be approximated by a Poisson distribution. We extend our
results to yield similar conclusions for $X_i$, the number of pairs  
of subsets
that overlap in exactly $i$ elements. Finally, we show that the joint
distribution $(X_0, X_1, ..., X_b)$ can be approximated by a  
multidimensional
Poisson vector with independent components.


http://front.math.ucdavis.edu/math.CO/0509382

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3780. TWO-PARAMETER $P, Q$-VARIATION PATHS AND INTEGRATIONS OF LOCAL  
TIMES

Chunrong Feng and  Huaizhong Zhao

In this paper, we prove two main results. The first one is to give a new
condition for the existence of two-parameter $p,q$-variation path  
integrals and
dominated convergence results for both the one-parameter and two- 
parameter
integrals. Our condition of locally bounded $p,q$-variation is more  
natural and
easy to verify than those of Young. The second result is to define  
the integral
of local time pathwise and then give generalized Ito's formula when
$\nabla^-f(s,x)$ is only of bounded $p,q$-variation in $(s,x)$. In  
the case
that $g(s,x)=\nabla^-f(s,x)$ is of locally bounded variation in $(s,x) 
$, the
integral $\int_{-\infty}^\infty\int_0^t \nabla^-f(s,x)d_{s,x}L_s(x)$  
is the
Lebesgue-Stieltjes integral and was used in Elworthy, Truman and Zhao  
(2004).
When $g(s,x)=\nabla^-f(s,x)$ is of only locally $p, q$-variation,  
where $p\geq
1$,$q\geq 1$, and $2q+1>2pq$, the integral is a two-parameter $p,1$- 
variation
path integral rather than a Lebesgue-Stieltjes integral. In the  
special case
that $f(s,x)=f(x)$ is independent of $s$, we give a new condition for  
Meyer's
formula and $\int_{-\infty}^\infty L_t(x)d_x\nabla^-f(x)$ is defined  
pathwise
as a Lyons-Young's integral of $p$-variation. For this we prove the  
local time
$L_t(x)$ is of $p$-variation in $x$ for each $t\geq 0$, for each $p>2 
$ almost
surely ($p$-variation in the sense of Young. Both results are new in  
rough path
theory and local time integration respectively.


http://front.math.ucdavis.edu/math.PR/0509422

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3781. A CENTRAL LIMIT THEOREM AND HIGHER ORDER RESULTS FOR THE  
ANGULAR   BISPECTRUM

D. Marinucci

The angular bispectrum of spherical random fields has recently gained an
enormous importance, especially in connection with statistical  
inference on
cosmological data. In this paper, we provide expressions for its  
moments of
arbitrary order and we use these results to establish a multivariate  
central
limit theorem and higher order approximations. The results rely upon
combinatorial methods from graph theory and a detailed investigation  
for the
asymptotic behaviour of Clebsch-Gordan coefficients; the latter are  
widely used
in representation theory and quantum theory of angular momentum.


http://front.math.ucdavis.edu/math.PR/0509430

---------------------------------------------------------------

3782. PRECISE FINITE-SAMPLE QUANTILES OF THE JARQUE-BERA ADJUSTED  
LAGRANGE   MULTIPLIER TEST

Diethelm Wuertz and Helmut G. Katzgraber

It is well known that the finite-sample null distribution of the  
Jarque-Bera
Lagrange Multiplier (LM) test for normality and its adjusted version  
(ALM)
introduced by Urzua differ considerably from their asymptotic chi^2 
(2) limit.
Here, we present results from Monte Carlo simulations using 10^7  
replications
which yield very precise numbers for the LM and ALM statistic over a  
wide range
of critical values and sample sizes. This enables a precise  
implementation of
the Jarque-Bera LM and ALM test for finite samples.


http://front.math.ucdavis.edu/math.ST/0509423

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3783. LINEAR FUNCTIONS ON THE CLASSICAL MATRIX GROUPS

Elizabeth Meckes

Let $M$ be a random matrix in the orthogonal group $\O_n$, distributed
according to Haar measure, and let $A$ be a fixed $n\times n$ matrix  
over $\R$
such that $\tr(AA^t)=n$. Then the total variation distance of the random
variable $\tr(AM)$ to standard normal is bounded by $2\sqrt{3}/(n-1) 
$, and this
rate is sharp up to the constant. Analogous results are obtained for  
$M$ a
random unitary matrix and $A$ a fixed $n\times n$ matrix over $\C$.  
The proofs
are via an improvement of Stein's method of exchangeable pairs which  
makes use
of the continuous nature of the symmetries of the classical matrix  
groups.


http://front.math.ucdavis.edu/math.PR/0509441

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3784. ZERO BIASING AND A DISCRETE CENTRAL LIMIT THEOREM

Larry Goldstein and Aihua Xia

We introduce a new family of distributions to approximate $\prob(W\in  
A)$ for
$A\subset\{...,-2,-1,0,1,2,...\}$ and $W$ a sum of independent  
integer-valued
random variables $\xi_1$, $\xi_2$, $...$, $\xi_n$ with finite second  
moments,
where with large probability $W$ is not concentrated on a lattice of  
span
greater than 1. The well-known Berry--Esseen theorem states that for  
$Z$ a
normal random variable with mean $\mean(W)$ and variance $\var(W)$, $ 
\prob(Z
\in A)$ provides a good approximation to $\prob(W \in A)$ for $A$ of  
the form
$(-\infty,x]$. However, for more general $A$ such as the set of all even
numbers, the normal approximation becomes unsatisfactory and it is  
desirable to
have an appropriate discrete, non-normal, distribution which  
approximates $W$
in total variation, and a discrete version of the Berry--Esseen  
theorem to
bound the error. In this paper, using the concept of zero biasing for  
discrete
random variables [cf Goldstein and Reinert (2005)], we introduce a  
new family
of discrete distributions and provide a discrete version of the  
Berry--Esseen
theorem showing how members of the family approximate the  
distribution of a sum
$W$ of integer valued variables in total variation.


http://front.math.ucdavis.edu/math.PR/0509444

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3785. ON A CLASS OF STOCHASTIC SEMILINEAR PDE'S

Luigi Manca

We consider stochastic semilinear partial differential equations with
Lipschitz nonlinear terms. We prove existence and uniqueness of an  
invariant
measure and the existence of a solution for the corresponding Kolmogorov
equation in the space $L^2(H;\nu)$, where $\nu$ is the invariant  
measure. We
also prove the closability of the derivative operator and an  
integration by
parts formula. Finally, under boundness conditions on the nonlinear  
term, we
prove a Poincar\'e inequality, a logarithmic Sobolev inequality and the
ipercontractivity of the transition semigroup.


http://front.math.ucdavis.edu/math.PR/0509446

---------------------------------------------------------------

3786. A CENTRAL LIMIT THEOREM AND HIGHER ORDER RESULTS FOR THE  
ANGULAR   BISPECTRUM

D. Marinucci

The angular bispectrum of spherical random fields has recently gained an
enormous importance, especially in connection with statistical  
inference on
cosmological data. In this paper, we provide expressions for its  
moments of
arbitrary order and we use these results to establish a multivariate  
central
limit theorem and higher order approximations. The results rely upon
combinatorial methods from graph theory and a detailed investigation  
for the
asymptotic behaviour of Clebsch-Gordan coefficients; the latter are  
widely used
in representation theory and quantum theory of angular momentum.


http://front.math.ucdavis.edu/math.PR/0509430

---------------------------------------------------------------

3787. SHY COUPLINGS

Itai Benjamini and  Krzysztof Burdzy and Zhen-Qing Chen

A pair of Markov processes is called a Markov coupling if both  
processes have
the same transition probabilities and the pair is also a Markov  
process. We say
that a coupling is ``shy'' if the processes never come closer than some
(random) strictly positive distance from each other. We investigate  
whether shy
couplings exist for several classes of Markov processes.


http://front.math.ucdavis.edu/math.PR/0509458

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3788. EXCITED RANDOM WALK AGAINST A WALL

Gideon Amir and  Itai Benjamini and Gady Kozma

We analyze random walk in the upper half of a three dimensional  
lattice which
goes down whenever it encounters a new vertex, a.k.a. excited random  
walk. We
show that it is recurrent with an expected number of returns of  
square-root log
n.


http://front.math.ucdavis.edu/math.PR/0509464

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3789. CONGRUENCE PROPERTIES OF DEPTHS IN SOME RANDOM TREES

Svante Janson

Consider a random recusive tree with n vertices. We show that the  
number of
vertices with even depth is asymptotically normal as n tends to  
infinty. The
same is true for the number of vertices of depth divisible by m for  
m=3, 4 or
5; in all four cases the variance grows linearly. On the other hand,  
for m at
least 7, the number is not asymptotically normal, and the variance  
grows faster
than linear in n. The case m=6 is intermediate: the number is  
asymptotically
normal but the variance is of order n log n.
   This is a simple and striking example of a type of phase  
transition that has
been observed by other authors in several cases. We prove, and  
perhaps explain,
this non-intuitive behavious using a translation to a generalized  
Polya urn.
   Similar results hold for a random binary search tree; now the  
number of
vertices of depth divisible by m is asymptotically normal for m at  
most 8 but
not for m at least 9, and the variance grows linearly in the first  
case both
faster in the second. (There is no intermediate case.)
   In contrast, we show that for conditioned Galton-Watson trees,  
including
random labelled trees and random binary trees, there is no such phase
transition: the number is asymptotically normal for every m.


http://front.math.ucdavis.edu/math.PR/0509471

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3790. PERCOLATING PATHS THROUGH RANDOM POINTS :

David Aldous and Maxim Krikun

We prove consistency of four different approaches to formalizing the  
idea of
minimum average edge-length in a path linking some infinite subset of  
points of
a Poisson process. The approaches are (i) shortest path from origin  
through
some $m$ distinct points; (ii) shortest average edge-length in paths  
across the
diagonal of a large cube; (iii) shortest path through some specified  
proportion
$\delta$ of points in a large cube; (iv) translation-invariant  
measures on
paths in $\Reals^d$ which contain a proportion $\delta$ of the  
Poisson points.
We develop basic properties of a normalized average length function $c 
(\delta)$
and pose challenging open problem


http://front.math.ucdavis.edu/math.PR/0509492

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3791. A FILTERING APPROACH TO TRACKING VOLATILITY FROM PRICES  
OBSERVED AT  RANDOM TIMES

Jaksa Cvitanic and  Robert Liptser and  Boris Rozovskii

This paper is concerned with nonlinear filtering of the coefficients  
in asset
price models with stochastic volatility. More specifically, we assume  
that the
asset price process $ S=(S_{t})_{t\geq0} $ is given by \[
dS_{t}=r(\theta_{t})S_{t}dt+v(\theta_{t})S_{t}dB_{t}, \] where
$B=(B_{t})_{t\geq0}$ is a Brownian motion, $v$ is a positive  
function, and
$\theta=(\theta_{t})_{t\geq0}$ is a c\'{a}dl\'{a}g strong Markov  
process. The
random process $\theta$ is unobservable. We assume also that the  
asset price
$S_{t}$ is observed only at random times $0<\tau_{1}<\tau_{2}<....$  
This is an
appropriate assumption when modelling high frequency financial data  
(e.g.,
tick-by-tick stock prices).
   In the above setting the problem of estimation of $\theta$ can be  
approached
as a special nonlinear filtering problem with measurements generated  
by a
multivariate point process $(\tau_{k},\log S_{\tau_{k}})$. While  
quite natural,
this problem does not fit into the standard diffusion or simple point  
process
filtering frameworks and requires more technical tools. We derive a  
closed form
optimal recursive Bayesian filter for $\theta_{t}$, based on the  
observations
of $(\tau_{k},\log S_{\tau_{k}})_{k\geq1}$. It turns out that the  
filter is
given by a recursive system that involves only deterministic  
Kolmogorov-type
equations, which should make the numerical implementation relatively  
easy.


http://front.math.ucdavis.edu/math.PR/0509503

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3792. OPERATORS ASSOCIATED WITH STOCHASTIC DIFFERENTIAL EQUATIONS  
DRIVEN BY  FRACTIONAL BROWNIAN MOTIONS

Fabrice Baudoin and  Laure Coutin

In this paper, by using a Taylor development type formula, we show  
how it is
possible to associate differential operators with stochastic  
differential
equations driven by a fractional Brownian motion. As an application,  
we deduce
that invariant measures for such SDEs must satisfy an infinite  
dimensional
system of partial differential equations.


http://front.math.ucdavis.edu/math.PR/0509511

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3793. GROWTH OF LEVY TREES

Thomas Duquesne (Paris 11) and  Matthias Winkel (Oxford)

We construct random locally compact real trees called Levy trees that  
are the
genealogical trees associated with continuous-state branching  
processes. More
precisely, we define a growing family of discrete Galton-Watson trees  
with
i.i.d. exponential branch lengths that is consistent under Bernoulli
percolation on leaves; we define the Levy tree as the limit of this  
growing
family with respect to the Gromov-Hausdorff topology on metric  
spaces. This
elementary approach notably includes supercritical trees and does not  
make use
of the height process introduced by Le Gall and Le Jan to code the  
genealogy of
(sub)critical continuous-state branching processes. We construct the  
mass
measure of Levy trees and we give a decomposition along the ancestral  
subtree
of a Poisson sampling directed by the mass measure.


http://front.math.ucdavis.edu/math.PR/0509518

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3794. CONTINUUM RANDOM TREES AND BRANCHING PROCESSES WITH IMMIGRATION

Thomas Duquesne (Paris11)

We study a genealogical model for continuous-state branching  
processes with
immigration with a (sub)critical branching mechanism. This model  
allows the
immigrants to be on the same line of descent. The corresponding  
family tree is
an ordered rooted continuum random tree with a single infinite end  
defined
thanks to two continuous processes denoted by $(\overleftarrow{H}_t ;t 
\geq 0)$
and $(\overrightarrow{H}_t ;t\geq 0)$ that code the parts at resp.  
the left and
the right hand of the infinite line of descent of the tree. These  
processes are
called the left and the right height processes. We define their local  
time
processes via an approximation procedure and we prove that they enjoy a
Ray-Knight property. We also discuss the important special case  
corresponding
to the size-biased Galton-Watson tree in the continuous setting. In  
the last
part of the paper we give a convergence result under general  
assumptions for
rescaled discrete left and right contour processes of sequences of
Galton-Watson trees with immigration. We also provide a strong  
invariance
principle for a sequence of rescaled Galton-Watson processes with  
immigration
that also holds in the supercritical case.


http://front.math.ucdavis.edu/math.PR/0509519

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3795. PATH DECOMPOSITIONS FOR REAL LEVY PROCESSES

Thomas Duquesne

Let $X$ be a real L\'evy process and let $\Xpos $ be the process  
conditioned
to stay positive. We assume that $ 0 $ is regular for $(-\infty, 0)$  
and $(0,
+\infty) $ with respect to $X$. Using elementary excursion theory  
arguments, we
provide a simple probabilistic description of the reversed paths of $X 
$ and
$\Xpos $ at their first hitting time of $ (x, +\infty)$ and last  
passage time
of $ (-\infty, x ] $, on a fixed time interval $[0, t]$, for a  
positive level
$x$. From these reversion formulas, we derive an extension to general  
L\'evy
processes of Williams' decomposition theorems, Bismut's decomposition  
of the
excursion above the infimum and also several relations involving the  
reversed
excursion under the maximum.


http://front.math.ucdavis.edu/math.PR/0509520