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作者：Fontes, LRG; Isopi, M; Newman, CM; Ravishankar, K
作者单位：Universidade de Sao Paulo; Sapienza University Rome; New York University; State University of New York (SUNY) System; University at Albany, SUNY
摘要：The Brownian web (BW) is the random network formally consisting of the paths of coalescing one-dimensional Brownian motions starting from every space-time point in R x R. We extend the earlier work of Arratia and of Toth and Werner by providing a new characterization which is then used to obtain convergence results for the BW distribution, including convergence of the system of all coalescing random walks to the BW under diffusive space-time scaling.
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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：Burdzy, K; Chen, ZQ; Sylvester, J
作者单位：University of Washington; University of Washington Seattle
摘要：The paper is concerned with reflecting Brownian motion (RBM) in domains with deterministic moving boundaries, also known as noncylindrical domains, and its connections with partial differential equations. Construction is given for RBM in C-3-smooth time-dependent domains in the n-dimensional Euclidean space R-n. We present various sample path properties of the process, two-sided estimates for its transition density function, and a probabilistic representation of solutions to some partial diffe...
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作者：Diaconis, P; Mayer-Wolf, E; Zeitouni, O; Zerner, MPW
作者单位：Stanford University; Stanford University; University of Minnesota System; University of Minnesota Twin Cities
摘要：We consider a Markov chain on the space of (countable) partitions of the interval [0, 1], obtained first by size-biased sampling twice (allowing repetitions) and then merging the parts (if the sampled parts are distinct) or splitting the part uniformly (if the same part was sampled twice). We prove a conjecture of Vershik stating that the Poisson-Dirichlet law with parameter theta = 1 is the unique invariant distribution for this Markov chain. Our proof uses a combination of probabilistic, com...
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作者：Burdzy, K; Kaspi, H
作者单位：University of Washington; University of Washington Seattle; Technion Israel Institute of Technology
摘要：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 star...
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作者：Bentkus, V
作者单位：Vilnius University; Vytautas Magnus University
摘要：In a celebrated work by Hoeffding [J. Amer Statist. Assoc. 58 (1963) 13-30], several inequalities for tail probabilities of sums Mn = X-1 +... + X-n of bounded independent random variables X-j were proved. These inequalities had a considerable impact on the development of probability and statistics, and remained unimproved until 1995 when Talagrand [Inst. Hautes Etudes Sci. Publ. Math. 81 (1995a) 73-205] inserted certain missing factors in the bounds of two theorems. By similar factors, a thir...
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作者：Houdré, C; Marchal, P
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris-Est-Creteil-Val-de-Marne (UPEC); University System of Georgia; Georgia Institute of Technology; Universite PSL; Ecole Normale Superieure (ENS)
摘要：Concentration of measure is studied, and obtained, for stable and related random vectors.
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作者：Comets, F; Zeitouni, O
作者单位：Universite Paris Cite; University of Minnesota System; University of Minnesota Twin Cities
摘要：We prove a law of large numbers for a class of ballistic, multidimensional random walks in random environments where the environment satisfies appropriate mixing conditions, which hold when the environment is a weak mixing field in the sense of Dobrushin and Shlosman. Our result holds if the mixing rate balances moments of some random times depending on the path. It applies in the nonnestling case, but we also provide examples of nestling walks that satisfy our assumptions. The derivation is b...
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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：Giné, E; Koltchinskii, V; Zinn, J
作者单位：University of Connecticut; University of Connecticut; University of New Mexico; Texas A&M University System; Texas A&M University College Station; University of Washington; University of Washington Seattle; Sorbonne Universite
摘要：Let fin denote a kernel density estimator of a continuous density f in d dimensions, bounded and positive. Let Psi(t) be a positive continuous function such that parallel toPsif(beta)parallel toinfinity < infinity for some 0 < beta < 1/2. Under natural smoothness conditions, necessary and sufficient conditions for the sequence rootnh(n)(d)/2\logh(n)(d)\ parallel toPsi(t)(f(n)(t) - Efn(t))parallel toinfinity to be stochastically bounded and to converge a.s. to a constant are obtained. Also, the...
