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作者：Estrade, Anne; Leon, Jose R.
作者单位：Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); University of Central Venezuela
摘要：We study the Euler characteristic of an excursion set of a stationary isotropic Gaussian random field X : Omega x R-d -> R. Let us fix a level u is an element of R and let us consider the excursion set above u, A(T, u) = {t is an element of T : X(t) >= u} where T is a bounded cube subset of R-d. The aim of this paper is to establish a central limit theorem for the Euler characteristic of A(T,u) as T grows to R-d, as conjectured by R. Adler more than ten years ago [Ann. Appl. Probab. 10 (2000) ...
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作者：Hutchcroft, Tom
作者单位：University of British Columbia
摘要：We prove that every component of the wired uniform spanning forest (WUSF) is one-ended almost surely in every transient reversible random graph, removing the bounded degree hypothesis required by earlier results. We deduce that every component of the WUSF is one-ended almost surely in every supercritical Galton Watson tree, answering a question of Benjamini, Lyons, Peres and Schramm [Ann. Probab. 29 (2001) 1-65]. Our proof introduces and exploits a family of Markov chains under which the orien...
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作者：Carmona, Rene; Delarue, Francois; Lacker, Daniel
作者单位：Princeton University; Princeton University; Universite Cote d'Azur; Universite Cote d'Azur
摘要：A theory of existence and uniqueness is developed for general stochastic differential mean field games with common noise. The concepts of strong and weak solutions are introduced in analogy with the theory of stochastic differential equations, and existence of weak solutions for mean field games is shown to hold under very general assumptions. Examples and counter-examples are provided to enlighten the underpinnings of the existence theory. Finally, an analog of the famous result of Yamada and...
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作者：Sheffield, Scott
作者单位：Massachusetts Institute of Technology (MIT)
摘要：We begin by studying inventory accumulation at a LIFO (last-in-first out) retailer with two products. In the simplest version, the following occur with equal probability at each time step: first product ordered, first product produced, second product ordered, second product produced. The inventory thus evolves as a simple random walk on Z(2). In more interesting versions, a p fraction of customers orders the freshest available product regardless of type. We show that the corresponding random w...
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作者：Kolb, Martin; Savov, Mladen
作者单位：University of Paderborn; Bulgarian Academy of Sciences
摘要：In this paper, we study the behavior of Brownian motion conditioned on the event that its local time at zero stays below a given increasing function f up to time T. For a class of nonincreasing functions f, we show that the conditioned process converges, as T -> infinity, to a limit process and we derive necessary and sufficient conditions for the limit to be transient. In the transient case, the limit process is described explicitly, and in the recurrent case we quantify the entropic repulsio...
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作者：Lee, James R.; Peres, Yuval; Smart, Charles K.
作者单位：University of Washington; University of Washington Seattle; Microsoft; University of Chicago
摘要：Consider a discrete-time martingale {X-t} taking values in a Hilbert space H. We show that if for some L >= 1, the bounds E[parallel to Xt+1 - X-t parallel to(2)(H)parallel to X-t] = 1 and parallel to Xt+1 - Xt+1 parallel to(H) <= L are satisfied for all times t >= 0, then there is a constant c = c(L) such that for 1 <= R <= root t, P(parallel to X-t-X0 parallel to(H) <= R) <= cR/root t . Following Lee and Peres [Ann. Probab. 41(2013) 3392-3419], this estimate has applications to small-ball es...
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作者：Xie, Longjie; Zhang, Xicheng
作者单位：Wuhan University
摘要：By establishing a characterization for Sobolev differentiability of random fields, we prove the weak differentiability of solutions to stochastic differential equations with local Sobolev and super-linear growth coefficients with respect to the starting point. Moreover, we also study the strong Feller property and the irreducibility to the associated diffusion semigroup.
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作者：Buraczewski, Dariusz; Collamore, Jeffrey F.; Damek, Ewa; Zienkiewicz, Jacek
作者单位：University of Wroclaw; University of Copenhagen
摘要：In a variety of problems in pure and applied probability, it is relevant to study the large exceedance probabilities of the perpetuity sequence Y-n := B-1 + A(1)B(2) + ... + (A(1) ...A(n-1))B-n, where (A(i), B-i) subset of (0, infinity) x R. Estimates for the stationary tail distribution of {Y-n} have been developed in the seminal papers of Kesten [Acta Math. 131 (1973) 207-248] and Goldie [Ann. Appl. Probab. 1 (1991) 126-166]. Specifically, it is well known that if M := sup(n) Y-n, then P{M >...
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作者：Dey, Partha S.; Zygouras, Nikos
作者单位：University of Illinois System; University of Illinois Urbana-Champaign; University of Warwick
摘要：The directed polymer model at intermediate disorder regime was introduced by Alberts-Khanin-Quastel [Ann. Probab. 42 (2014) 1212-1256]. It was proved that at inverse temperature beta n(-gamma) with gamma = 1/4 the partition function, centered appropriately, converges in distribution and the limit is given in terms of the solution of the stochastic heat equation. This result was obtained under the assumption that the disorder variables posses exponential moments, but its universality was also c...
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作者：Fournier, Nicolas; Hauray, Maxime
作者单位：Sorbonne Universite; Aix-Marseille Universite
摘要：We consider the 3D Landau equation for moderately soft potentials [gamma is an element of (-2, 0) with the usual notation] as well as a stochastic system of N particles approximating it. We first establish some strong/weak stability estimates for the Landau equation, which are fully satisfactory only when gamma is an element of [-1, 0). We next prove, under some appropriate conditions on the initial data, the so-called propagation of molecular chaos, that is, that the empirical measure of the ...
