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作者：COURBAGE, M; HAMDAN, D
摘要：We study the class C-pi of probability measures invariant with respect to the shift transformation on K-Z (where K is a finite set of integers) which satisfies the Chapman-Kolmogorov equation for a given stochastic matrix Pi. We construct a dense subset of measures in C-pi distinct from the Markov measure. When Pi is irreducible and aperiodic, these measures are ergodic but not weakly mixing. We show that the set of measures with infinite memory is G(delta) dense in C-pi and that the Markov me...
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作者：DEMASI, A; PELLEGRINOTTI, A; PRESUTTI, E; VARES, ME
作者单位：University of Rome Tor Vergata; Sapienza University Rome
摘要：We consider a one-dimensional Glauber-Kawasaki process which gives rise in the hydrodynamical limit to a reaction diffusion equation with a double-well potential. We study the case when the process starts off from a product measure with zero averages, which, hydrodynamically, corresponds to a stationary unstable state. We prove that at times longer than the hydrodynamical ones the reaction diffusion equation no longer describes the behavior of the system, which in fact leaves the unstable equi...
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作者：PEMANTLE, R; PERES, Y
作者单位：Yale University; Oregon State University
摘要：We define a notion of stochastic domination between trees, where one tree dominates another if, when the vertices of each are labeled with independent, identically distributed random variables, one tree is always more likely to contain a path with a specified property. Sufficient conditions for this kind of domination are (1) more symmetry and (2) earlier branching. We apply these conditions to the problem of determining how fast a tree must grow before first-passage percolation on the tree ex...
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作者：BOLTHAUSEN, E
摘要：We consider an ordinary, symmetric, continuous-time random walk on the two-dimensional lattice Z2. The distribution of the walk is transformed by a density which discounts exponentially the number of points visited up to time T. This introduces a self-attracting interaction of the paths. We study the asymptotic behavior for T --> infinity. It turns out that the displacement is asymptotically of order T1/4. The main technique for proving the result is a refined analysis of large deviation proba...
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作者：DUPUIS, P; WILLIAMS, RJ
作者单位：University of California System; University of California San Diego
摘要：We prove that a sufficient condition for a semimartingale reflecting Brownian motion in an orthant (SRBM) to be positive recurrent is that all solutions of an associated deterministic Skorokhod problem are attracted to the origin. To prove this result, we construct a Lyapunov function for the SRBM.
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作者：COX, JT; GREVEN, A
作者单位：University of Gottingen
摘要：Let x(t) = {x(i)(t), i is-an-element-to Z(d)} be the solution of the system of stochastic differential equations dx(i)(t) = (SIGMA(j is-an-element-of Z(d) a (i, j)x(j)(t) - x(i)(t)) dt + square-root 2g(x(i)(t)) dw(i)(t), i is-an-element-of Z(d). Here g: [0, 1] - R+ satisfies g > 0 on (0, 1), g(0) = g(1) = 0, g is Lipschitz, a(i,j) is an irreducible random walk kernel on Z(d) and {w(i)(t), i is-an-element-of Z(d)) is a family of standard, independent Brownian motions on R; x(t) is a Markov proc...
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作者：HITCZENKO, P
摘要：It is known that if (X(n)) and (Y(n)) are two (F(n))-adapted sequences of random variables such that for each k greater-than-or-equal-to 1 the conditional distributions of X(k) and Y(k), given F(k-1), coincide a.s., then the following is true: \\SIGMAX(k)\\p less-than-or-equal-to B(p)\\SIGMA Y(k)\\p, 1 less-than-or-equal-to p < infinity, for some constant B(p) depending only on p. The aim of this paper is to show that if a sequence (Y(n)) is conditionally independent, then the constant B(p) ma...
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作者：STEIF, JE
摘要：We consider the threshold voter automaton in one dimension with threshold tau > n/2, where n is the number of neighbors and where we start from a product measure with density 1/2. It has recently been shown that there is a critical value theta(c) approximate to 0.6469076, so that if tau = theta n with theta > theta(c) and n is large, then most sites never flip, while for theta epsilon (1/2, theta(c)) and n large, there is a limiting state consisting mostly of large regions of points of the sam...
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作者：LU, SL
摘要：We study equilibrium fluctuations for hydrodynamic limits of a nongradient Ginzburg-Landau model. We prove that the limit fluctuation process is governed by a generalized stationary Ornstein-Uhlenbeck process.
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作者：TALAGRAND, M
作者单位：University System of Ohio; Ohio State University
摘要：We show that the logarithm of the probability that the Brownian sheet has a supremum at most epsilon over [0, 1](2) is of order epsilon(-2)(log(1/epsilon))(3).
