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作者：Davie, G
作者单位：University of South Africa
摘要：We formulate effective versions of the Borel-Cantelli lemmas using a coefficient from Kolmogorov complexity. We then use these effective versions to lift the effective content of the law of large numbers and the law of the iterated logarithm.
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作者：Krylov, NV
作者单位：University of Minnesota System; University of Minnesota Twin Cities
摘要：The distributions of stochastic integrals are approximated by the distributions of stochastic integrals of piece-wise constant processes. The rate of approximation in some negative Sobolev spaces is estimated. Generalizations are given for problems arising in control theory.
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作者：Mason, DM; Shao, QM
作者单位：University of Delaware; University of Oregon
摘要：Let X-1,..., X-n, n greater than or equal to 1, be independent, identically distributed random variables and consider the Student t-statistic T-n based upon these random variables. Gine, Gotze and Mason (1997) proved that T-n converges in distribution to a standard normal random variable if and only if X is in the domain of attraction of a normal random variable and EX = 0. We shall show that roughly the same holds true for the bootstrapped Student t-statistic T-n*. In the process we shall dis...
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作者：Chassaing, P; Janson, S
作者单位：Universite de Lorraine; Uppsala University
摘要：We describe a Vervaat-like path transformation for the reflected Brownian bridge conditioned on its local time at 0: up to random shifts, this process equals the two processes constructed from a Brownian bridge and a Brownian excursion by adding a drift and then taking the excursions over the current minimum. As a consequence, these three processes have the same occupation measure, which is easily found. The three processes arise as limits, in three different ways, of profiles associated to ha...
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作者：Jonasson, J
作者单位：University of Gothenburg; Chalmers University of Technology
摘要：We consider a version of the Boolean (or Poisson blob) continuum percolation model where, at each point of a Poisson point process in the Euclidean plane with intensity lambda, a copy of a given compact convex set A with fixed rotation is placed. To each A we associate a critical value lambda (c)(A) which is the infimum of intensities lambda for which the occupied component contains an unbounded connected component. It is shown that min{lambda (c)(A) : A convex of area a} is attained if A is a...
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作者：Caputo, P; Deuschel, JD
作者单位：Technical University of Berlin
摘要：We continue our study of large deviations of the empirical measures of a massless Gaussian field on Z(d), whose covariance is given by the Green function of a long-range random walk. In this paper we extend techniques and results of Bolthausen and Deuschel to the nonlocal case of a random walk in the domain of attraction of the symmetric alpha -stable law, with alpha epsilon (0, 2 boolean AND d). In particular, we show that critical large deviations occur at the capacity scale Nd-alpha, With a...
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作者：Dynkin, EB
作者单位：Cornell University
摘要：Superprocesses (under the name continuous state branching processes) appeared, first, in a pioneering work of S. Watanabe [J. Math.. Kyoto Univ. 8 (1968) 141-167]. Deep results on paths of the super-Brownian motion were obtained by Dawson, Perkins, Le Gall and others. In earlier papers, a superprocess was interpreted as a Markov process X-t in the space of measures. This is not sufficient for a probabilistic approach to boundary value problems. A reacher model based on the concept of exit meas...
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作者：Giacomin, G; Olla, S; Spohn, H
作者单位：Universite Paris Cite; CY Cergy Paris Universite; Institut Polytechnique de Paris; Ecole Polytechnique; Technical University of Munich; University of Munich; Technical University of Munich
摘要：We study the large scale space-time fluctuations of an interface which is modeled by a massless scalar field with reversible Langevin dynamics. For a strictly convex interaction potential we prove that on a large space-time scale these fluctuations are governed by an infinite-dimensional Ornstein-Uhlenbeek process. Its effective diffusion type covariance matrix is characterized through a variational formula.
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作者：Burdzy, K; Chen, ZQ
作者单位：University of Washington; University of Washington Seattle
摘要：We define a local time flow of skew Brownian motions, that is, a family of solutions to the stochastic differential equation defining the skew Brownian motion, starting from different points but driven by the same Brownian motion. We prove several results on distributional and path properties of the flow. Our main result is a version of the Ray-Knight theorem on local times. In our case, however, the local time process viewed as a function of the spatial variable is a pure jump Markov process ...
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作者：Sznithman, AS
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We introduce in this article a class of transient random walks in a random environment on Z(d). When d greater than or equal to 2, these walks are ballistic and we derive a law of large numbers, a central limit theorem and large-deviation estimates. In the so-called nestling situation, large deviations in the neighborhood of the segment [0, v], v being the limiting velocity, are critical. They are of special interest in view of their close connection with the presence of traps in the medium, t...
