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作者：DeBlassie, D
作者单位：Texas A&M University System; Texas A&M University College Station
摘要：For continuous gamma, g:[0, 1] --> (0, infinity), 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 g(1)/gamma(2)(1) > root2 -1 . When specialized to a case studied by Swart [Stochastic Process. Appl. 98 (2002) 131-149] with gamma = root2 and g equivalent to c, this gives an improvement of his result. ...
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作者：Asselah, A; Pra, PD
作者单位：Aix-Marseille Universite; University of Padua
摘要：We consider the symmetric exclusion process {eta(t), t > 0} on {0,1}(Zd). We fix a pattern A := {eta: Sigma(Lambda) eta(i) greater than or equal to k}, where Lambda is a finite subset of Z(d) and k is an integer, and we consider the problem of establishing sharp estimates for tau, the hitting time of A. We present a novel argument based on monotonicity which helps in some cases to obtain sharp tail asymptotics for tau in a simple way. Also, we characterize the trajectories {eta(s), s less than...
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作者：Bobkov, SG
作者单位：University of Minnesota System; University of Minnesota Twin Cities
摘要：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.
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作者：Bass, RF; Chen, X
作者单位：University of Connecticut; University of Tennessee System; University of Tennessee Knoxville
摘要：If beta(t). is renormalized self-intersection local time for planar Brownian motion, we characterize when Ee(gammabeta1) 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 --> infinity.
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作者：Hu, YY; Shi, Z
作者单位：Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Sorbonne Universite
摘要：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 proble...
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作者：Aida, S
作者单位：University of Osaka
摘要：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.
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作者：Barlow, MT
作者单位：University of British Columbia
摘要：We obtain Gaussian upper and lower bounds on the transition density q(t)(x, y) of the continuous time simple random walk on a supercritical percolation cluster C(infinity) in the Euclidean lattice. The bounds, analogous to Aronsen's bounds for uniformly elliptic divergence form diffusions, hold with constants c(i) depending only on p (the percolation probability) and d. The irregular nature of the medium means that the bound for q(t) (x, (.)) holds only for t greater than or equal to S(x) (ome...
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作者：Chen, X
作者单位：University of Tennessee System; University of Tennessee Knoxville
摘要：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 greater than or equal to 2, we prove lim(t-->infinity) t(-1) logP{alpha([0, 1](P)) greater than or equal to t((d(p-1))/2)} = -gammaalpha(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...
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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：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...
