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作者：FELDMAN, RE; RACHEV, S
摘要：Limiting distributions of square-integrable infinite order U-statistics were first studied by Dynkin and Mandelbaum and Mandelbaum and Taqqu. We extend their results to the case of non-Poisson random sample size. Multiple integrals of non-Gaussian generalized fields are constructed to identify the limiting distributions. An invariance principle is also established. We use these results to study the limiting distribution of the amount of charge left in some set by an infinite system of signed M...
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作者：EINMAHL, U
摘要：A general bounded law of the iterated logarithm for Banach space valued random variables is established. Our result implies: (a) the bounded LIL of Ledoux and Talagrand, (b) a bounded LIL for random variables in the domain of attraction of a Gaussian law and (c) new LIL results for random variables outside the domain of attraction of a Gaussian law in cases where the classical norming sequence {root nLLn} does not work. Basic ingredients of our proof are an infinite-dimensional Fuk-Nagaev type...
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作者：MUELLER, C
摘要：We consider the heat equation with a noise term, on a finite interval with periodic boundary conditions. We show how to construct coupled solutions to the equation. As applications, we prove the uniqueness of invariant measures and the triviality of bounded harmonic functions.
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作者：DIACONIS, P; SALOFFCOSTE, L
作者单位：Centre National de la Recherche Scientifique (CNRS); Sorbonne Universite
摘要：We develop techniques for bounding the rate of convergence of a symmetric random walk on a finite group to the uniform distribution. The techniques gives bounds on the second largest (and other) eigenvalues in terms of the eigenvalues of a comparison chain with known eigenvalues. The techniques yield sharp rates for a host of previously intractable problems on the symmetric group.
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作者：GEORGII, HO
摘要：We present a new approach to the principle of large deviations for the empirical field of a Gibbsian random field on the integer lattice Z(d). This approach has two main features. First, we can replace the traditional weak topology by the finer topology of convergence of cylinder probabilities, and thus obtain estimates which are finer and more widely applicable. Second, we obtain as an immediate consequence a limit theorem for conditional distributions under conditions on the empirical field,...
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作者：BHATT, AG; KARANDIKAR, RL
摘要：We extend Echeverria's criterion for invariant measures for a Markov process characterized via martingale problems to the case where the state space of the Markov process is a complete separable metric space. Essentially, the only additional conditions required are a separability condition on the operator occurring in the martingale problem and the well-posedness of the martingale problem in the class of progressively measurable solutions (as opposed to well-posedness in the class of r.c.l.l. ...
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作者：CSORGO, M; SHAO, QM
作者单位：Zhejiang University
摘要：Based on the well-known Borell inequality and on a general theorem for large and small increments of Banach space valued stochastic processes of Csaki, Csorgo and Shao, we establish some almost sure path behaviour of increments in general, and moduli of continuity in particular, for l(p)-valued, 1 less than or equal to p < infinity, Gaussian processes with stationary increments. Applications to l(p)-valued fractional Wiener and Ornstein-Uhlenbeck processes are also discussed. Our results refin...
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作者：CHEN, X
摘要：In this paper we establish some general forms of the law of the iterated logarithm for independent random variables (X(n)) with Banach space values, where (X(n)) is not necessarily identically distributed. Our results include the Kolmogorov law of the iterated logarithm (LIL) in both finite and infinite dimensional cases, and they improve the Wittmann LIL as well as extend it to the vector setting. The Ledoux-Talagrand LIL for an i.i.d. sequence is also a simple corollary of our results.
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作者：NGUYEN, BG; YANG, WS
作者单位：Pennsylvania Commonwealth System of Higher Education (PCSHE); Temple University
摘要：In this paper, we apply the Brydges-Spencer lace expansion and the Hara-Slade analysis to obtain the triangle condition for the nearest-neighbor oriented bond percolation in high dimensions and for the spread-out oriented bond percolation in Z(d) X Z, d greater than or equal to 5. Furthermore, we also establish the infrared bound in the subcritical region and the mean-field behavior for these models.
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作者：DILWORTH, SJ; MONTGOMERYSMITH, SJ
作者单位：University of Missouri System; University of Missouri Columbia
摘要：Let X = Sigma epsilon(n)x(n) be a Rademacher series with vector-valued coefficients. We obtain an approximate formula for the distribution of the random variable parallel to X parallel to in terms of its mean and a certain quantity derived from the K-functional of interpolation theory. Several applications of the formula are given.
