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作者：Zhao, Ou; Woodroofe, Michael
作者单位：University of Michigan System; University of Michigan
摘要：There has been recent interest in the conditional central limit question for (strictly) stationary, ergodic processes ...., X-1, X-0, X-1 ,... whose partial sums S-n = X-1 + ... + X-n are of the form S-n = M-n + R-n, where M-n is a square integrable martingale with stationary increments and R-n is a remainder term for which E(R-n(2)) = o(n). Here we explore the law of the iterated logarithm (LIL) for the same class of processes. Letting parallel to center dot parallel to denote the norm in L-2...
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作者：Bertoin, J.; Doney, R. A.; Maller, R. A.
作者单位：Sorbonne Universite; University of Manchester; Australian National University; Australian National University
摘要：We wish to characterize when a Levy process X, crosses boundaries like t(k), K > 0, in a one- or two-sided sense, for small times t; thus, we inquire when lim sup(t down arrow 0) vertical bar X-t vertical bar/t(k), lim sup(t down arrow 0) X-t/t(k) and/or lim inf(t down arrow 0) X-t/t(k) are almost surely (a.s.) finite or infinite. Necessary and sufficient conditions are given for these possibilities for all values Of K > 0. This completes and extends a line of research going back to Blumenthal...
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作者：Bovier, Anton; Faggionato, Alessandra
作者单位：Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics; Technical University of Berlin; Sapienza University Rome
摘要：Sinai's walk can be thought of as a random walk on Z with random potential V, with V weakly converging under diffusive rescaling to a two-sided Brownian motion. We consider here the generator L-N of Sinai's walk on [-N, N] boolean AND Z with Dirichlet conditions on -N, N. By means of potential theory, for each h > 0, we show the relation between the spectral properties of L-N for eigenvalues of order o(exp(-h root N)) and the distribution of the h-extrema of the rescaled potential V-N(x) V(Nx)...
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作者：Chistyakov, G. P.; Goetze, F.
作者单位：National Academy of Sciences Ukraine; B. Verkin Institute for Low Temperature Physics & Engineering of the National Academy of Sciences of Ukraine; University of Bielefeld
摘要：Based on an analytical approach to the definition of additive free convolution on probability measures on the real line, we prove free analogues of limit theorems for sums for nonidentically distributed random variables in classical probability theory.
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作者：Schreiber, T.; Yukich, J. E.
作者单位：Nicolaus Copernicus University; Lehigh University
摘要：We show that the random point measures induced by vertices in the convex hull of a Poisson sample on the unit ball, when properly scaled and centered, converge to those of a mean zero Gaussian field. We establish limiting variance and covariance asymptotics in terms of the density of the Poisson sample. Similar results hold for the point measures induced by the maximal points in a Poisson sample. The approach involves introducing a generalized spatial birth growth process allowing for cell ove...
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作者：Sznitman, Alain-Sol
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We investigate the disconnection time of a simple random walk in a discrete cylinder with a large finite connected base. In a recent article of A. Dembo and the author it was found that for large N the disconnection time of G(N) x Z has rough order vertical bar GN vertical bar(2), when G(N) = (Z/NZ)(d). In agreement with a conjecture by I. Benjamini, we show here that this behavior has broad generality when the bases of the discrete cylinders are large connected graphs of uniformly bounded deg...
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作者：Benes, Christian
作者单位：Tufts University
摘要：We study two variants of the notion of holes formed by planar simple random walk of time duration 2n and the areas associated with them. We prove in both cases that the number of holes of area greater than A(n), where (A (n)) is an increasing sequence, is, up to a logarithmic correction term, asymptotic to n center dot A(n)(-1) for a range of large holes, thus confirming an observation by Mandelbrot. A consequence is that the largest hole has an area which is logarithmically asymptotic to n. W...
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作者：Antunes, Nelson; Fricker, Christine; Robert, Philippe; Tibi, Danielle
作者单位：Universidade do Algarve; Universite Paris Cite
摘要：This paper analyzes stochastic networks consisting of a set of finite capacity sites where different classes of individuals move according to some routing policy. The associated Markov jump processes are analyzed under a thermodynamic limit regime, that is, when the networks have some symmetry properties and when the number of nodes goes to infinity. An intriguing stability property is proved: under some conditions on the parameters, it is shown that, in the limit, several stable equilibrium p...
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作者：Decreusefond, Laurent; Nualart, David
作者单位：IMT - Institut Mines-Telecom; Institut Polytechnique de Paris; Telecom Paris; University of Kansas
摘要：We establish a general formula for the Laplace transform of the hitting times of a Gaussian process. Some consequences are derived, and particular cases like the fractional Brownian motion are discussed.
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作者：Zhang, Yu
作者单位：University of Colorado System; University of Colorado at Colorado Springs
摘要：We consider the first passage percolation model on Z(2). In this model, we assign independently to each edge e a passage time t(e) with a common distribution F. Let T(u, v) be the passage time from u to v. In this paper, we show that, whenever F(0) < p(c), sigma(2)(T((0, 0), (n, 0))) >= C log n for all n >= 1. Note that if F satisfies an additional special condition, inf supp(F) = r > 0 and F(r) > (p) over right arrow (c), it is known that there exists M such that for all n, sigma(2)(T((0, 0),...
