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作者：Hara, T; Van Der Hofstad, R; Slade, G
作者单位：Nagoya University; University of British Columbia; Delft University of Technology; Eindhoven University of Technology
摘要：We consider spread-out models of self-avoiding walk, bond percolation, lattice trees and bond lattice animals on Z(d), having long finite-range connections, above their upper critical dimensions d = 4 (self-avoiding walk), d = 6 (percolation) and d = 8 (trees and animals). The two-point functions for these models are respectively the generating function for self-avoiding walks from the origin to X E Zd, the probability of a connection from 0 to x, and the generating function for lattice trees ...
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作者：van der Hofstad, R; den Hollander, F; König, W
作者单位：Eindhoven University of Technology; Technical University of Berlin
摘要：In this article, we prove a large deviation principle for the empirical drift of a one-dimensional Brownian motion with self-repellence called the Edwards model. Our results extend earlier work in which a law of large numbers and a central limit theorem were derived. In the Edwards model, a path of length T receives a penalty e-(betaHT), where H-T is the self-intersection local time of the path and P E (0, 00) is a parameter called the strength of self-repellence. We identify the rate function...
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作者：Hino, M; Ramírez, JA
作者单位：Kyoto University; Cornell University
摘要：This work is involved with the short-time asymptotics of diffusion semigroups in a general setting. A generalization of Fang's version of Varadhan's formula is proven for general Dirichlet spaces that are local and conservative. The intrinsic metric appearing in the formula is characterized by pointwise distance for canonical Dirichlet spaces on loop groups.
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作者：Mytnik, L; Perkins, E
作者单位：Technion Israel Institute of Technology; University of British Columbia
摘要：This paper establishes the continuity of the density of (1 + beta)-stable super-Brownian motion (0 < beta < 1) for fixed times in d = 1, and local unboundedness of the density in all higher dimensions where it exists. We also prove local unboundedness of the density in time for a fixed spatial parameter in any dimension where the density exists, and local unboundedness of the occupation density (the local time) in the spatial parameter for dimensions d greater than or equal to 2 where the loca...
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作者：Khoshnevisan, D; Xiao, YM; Zhong, YQ
作者单位：Utah System of Higher Education; University of Utah; Michigan State University; Chinese Academy of Sciences
摘要：The primary goal of this paper is to study the range of the random field X (t) = Sigma(j=1)(N) X-j (t(j)), where X-1,...,X-N are independent Levy processes in R-d. To cite a typical result of this paper, let us suppose that psi(i) denotes the Levy exponent of X-i for each i = 1,...,N. Then, under certain mild conditions, we show that a necessary and sufficient condition for X(RN) to have positive d-dimensional Lebesgue measure is the integrability of the function R-d There Exists xi bar right ...
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作者：Gradinaru, M; Russo, F; Vallois, P
作者单位：Universite de Lorraine; Universite Paris 13
摘要：Given a locally bounded real function g, we examine the existence of a 4-covariation [g(B-H), BH, BH, BH], where BH is a fractional Brownian motion with a Hurst index H greater than or equal to (1)/(4). We provide two essential applications. First, we relate the 4-covariation to one expression involving the derivative of local time, in the case H = (1)/(4), generalizing an identity of Bouleau-Yor type, well known for the classical Brownian motion. A second application is an Ito formula of Stra...
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作者：Revelle, D
作者单位：University of California System; University of California Berkeley
摘要：This article examines the rate of escape for a random walk on G Z and proves laws of the iterated logarithm for both the inner and outer radius of escape. The class of G for which these results hold includes finite, G as well as groups of the form H Z, so the construction can be iterated. Laws of the iterated logarithm are also found for random walk on Baumslag-Solitar groups and a discrete version of the Sol geometry.
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作者：Li, WBV
作者单位：University of Delaware
摘要：Consider the first exit time tau(D) of a (d + 1)-dimensional Brownian motion from an unbounded open domain D = {(x, y) is an element of Rd+1 : y > f(x), x is an element of R-d} starting at (x(0), f(x(0)) + 1) is an element of Rd+1 for some x(0) is an element of R-d, where the function f(x) on R-d is convex and f(x) --> infinity as the Euclidean norm \x\ --> infinity. Very general estimates for the asymptotics of logP(tau(D) > t) are given by using Gaussian techniques. In particular, for f(x) e...
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作者：Burdzy, K; Kulczycki, T
作者单位：University of Washington; University of Washington Seattle; Polish Academy of Sciences; Wroclaw University of Science & Technology
摘要：Let X(t) be the symmetric alpha-stable process in R-d, alpha is an element of (0, 2), d greater than or equal to 2. For f:(0, 1) --> (0, infinity) let D (f) be the thorn {x is an element of R-d : x(1) is an element of (0, 1), \(x(2), - - -, x(d))\ < f (x(1))}. We give an integral criterion in terms of f for the existence of a random time s such that X(t) remains in X(s) + (D) over bar (f) for all t is an element of [s, s + 1).
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作者：Talagrand, M
作者单位：Sorbonne Universite; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); University System of Ohio; Ohio State University
摘要：Given a bounded class of functions, we introduce a combinatorial quantity (related to the idea of Vapnik-Chervonenkis classes) that is much more explicit than the Koltchinskii-Pollard entropy, but is proved to be essentially of the same order.
