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作者：Wu, JM
作者单位：University of Illinois System; University of Illinois Urbana-Champaign
摘要：Let X (t) be the symmetric alpha-stable process in R-d (0 < alpha < 2, d greater than or equal to 2). Then let W(f) be the thorn {x is an element of R-d:0 < x(1) < 1, (x(2)(2) +... + x(d)(2))(1)/(2) < f(x(1))} where f : (0, 1) --> (0, 1) is continuous, increasing with f (0(+)) = 0. Recently Burdzy and Kulczycki gave an exact integral condition on f for the existence of a random time s such that X(t) remains in the thorn X(s) + W(f) for all t is an element of [s, s + 1). We extend their theorem...
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作者：Lifshits, MA; Shi, Z
作者单位：Saint Petersburg State University; Sorbonne Universite; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：Consider a simple symmetric random walk on the integer lattice Z. For each n, let V(n) denote a favorite site (or most visited site) of the random walk in the first n steps. A somewhat Surprising theorem of Bass and Griffin [Z. Wahrsch. Verw. Gebiete 70 (1985) 417-436] says that V is almost surely transient, thus disproving a previous conjecture of Erdos and Revesz [Mathematical Structures-Computational Mathematics-Mathematical Modeling 2 (1984) 152-157]. More precisely, Bass and Griffin prove...
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作者：Albeverio, S; Kondratiev, Y; Pasurek, T; Röckner, M
作者单位：University of Bonn; University of Bielefeld; University of Bielefeld
摘要：We present a new method to prove existence and uniform a priori estimates for Euclidean Gibbs measures corresponding to quantum anharmonic crystals. It is based first on the alternative characterization of Gibbs measures in terms of their logarithmic derivatives through integration by parts formulas, and second on the choice of appropriate Lyapunov functionals.
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作者：Zambotti, L
作者单位：Scuola Normale Superiore di Pisa; University of Bielefeld
摘要：We consider the solution (u, eta) of the white-noise driven stochastic partial differential equation with reflection on the space interval [0, 1] introduced by Nualart and Pardoux, where eta is a reflecting measure on [0, infinity) x (0, 1) which forces the continuous function u, defined on [0, infinity) x [0, 1], to remain nonnegative and eta has support in the set of zeros of u. First, we prove that at any fixed time t > 0, the measure eta([0, t] x dtheta) is absolutely continuous w.r.t. the...
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作者：Dolgopyat, D; Kaloshin, V; Koralov, L
作者单位：University System of Maryland; University of Maryland College Park; California Institute of Technology; Princeton University
摘要：We consider a stochastic flow driven by a finite-dimensional Brownian motion. We show that almost every realization of such a flow exhibits strong statistical properties such as the exponential convergence of an initial measure to the equilibrium state and the central limit theorem. The proof uses new estimates of the mixing rates of the multi-point motion.
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作者：Piau, D
作者单位：Universite Claude Bernard Lyon 1
摘要：The immortal branching Markov process (iBMP) is a modification of the usual branching model, in which each particle of generation 17 is counted, in addition to its offspring, as a member of generation n + 1, its state being unchanged. When the number of offspring is Bernoulli, iBMP accounts, for instance, for the variability of the biological sequences that are produced by polymerase chain reactions (PCRs). This variability is due to the mutations and to the incomplete replications that affect...
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作者：Alexander, KS
作者单位：University of Southern California
摘要：An infinite-volume mixing or exponential-decay property in a spin system or percolation model reflects the inability of the influence of the configuration in one region to propagate to distant regions, but in some circumstances where such properties hold, propagation can nonetheless occur in finite volumes endowed with boundary conditions. We establish the absense of such propagation, particularly in two dimensions in finite volumes which are simply connected, under a variety of conditions, ma...
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作者：Hu, YZ; Mohammed, SEA; Yan, F
作者单位：University of Kansas; Southern Illinois University System; Southern Illinois University
摘要：In this paper, we develop a strong Milstein approximation scheme for solving stochastic delay differential equations (SDDEs). The scheme has convergence order 1. In order to establish the scheme, we prove an infinite-dimensional Ito formula for tame functions acting on the segment process of the solution of an SDDE. It is interesting to note that the presence of the memory in the SDDE requires the use of the Malliavin calculus and the anticipating stochastic analysis of Nualart and Pardoux. Gi...
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作者：Engländer, J; Kyprianou, AE
作者单位：University of California System; University of California Santa Barbara; Utrecht University
摘要：Let X be either the branching diffusion corresponding to the operator Lu + beta(u(2) - u) on D subset of or equal to R-d [where beta(x) greater than or equal to 0 and beta not equivalent to 0 is bounded from above] or the superprocess corresponding to the operator Lu + betau - alphau(2) on D subset of or equal to R-d (with alpha > 0 and beta is bounded from above but no restriction on its sign). Let lambda(c) denote the generalized principal eigenvalue for the operator L + beta on D. We prove ...
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作者：Li, WV; Shao, QM
作者单位：University of Delaware; University of Oregon
摘要：Let X = (X-t)(tis an element ofS) be a real-valued Gaussian random process indexed by S with mean zero. General upper and lower estimates are given for the lower tail probability P(sup(tis an element ofS)(X-t - X-t0) less than or equal to x) as x --> 0, with t(0) is an element of S fixed. In particular, sharp rates are given for fractional Brownian sheet. Furthermore, connections between lower tail probabilities for Gaussian processes with stationary increments and level crossing probabilities...
