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作者：YU, Z
摘要：Consider a special independent bond percolation model on Z2, in which all bonds with vertices in the X axis are open with probability delta and closed with probability 1 - delta, and all other bonds are open with probability p and closed with probability 1 - p. In this paper we show that no percolation occurs at p(c) for any delta < 1. The method allows us also to show no percolation at p(c) in a more general inhomogeneous case.
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作者：MARCUS, MB; ROSEN, J
作者单位：City University of New York (CUNY) System; College of Staten Island (CUNY); Texas A&M University System; Texas A&M University College Station
摘要：Both standard and functional laws of the iterated logarithm are obtained for the local time of a symmetric Levy process, at a fixed point in its state space, as time goes to infinity. Similar results are also obtained for the difference of the local times at two points in the state space. These results are sharp if the exponent of the characteristic function that defines the Levy process is regularly varying at zero with index 1 < beta less-than-or-equal-to 2. The results are given in terms of...
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作者：KRISTIANSEN, GK
摘要：A proof is given of a conjecture, due to F. W. Steutel: the set of positive alpha-values, for which any positive mixture of GAMMA(alpha)-distributions is infinitely divisible, is the interval (0, 2].
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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：CHENG, R
摘要：It is shown that a regular stationary random field on Z2 exhibits the weak (strong) commutation property if and only if its spectral density is the squared modulus of a weakly (strongly) outer function in the Hardy space H-2(T2) of the torus. Applications to prediction are discussed.
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作者：PINSKY, M; PINSKY, RG
作者单位：Technion Israel Institute of Technology
摘要：Let sigma(t) be an ergodic Markov chain on a finite state space E and for each sigma is-an-element-of E, define on R(d) the second-order elliptic operator [GRAPHICS] Then for each realization sigma(t) = sigma(t,omega) of the Markov chain, L(sigma(t)) may be thought of as a time-inhomogeneous diffusion generator. We call such a Process a diffusion in a random temporal environment or simply a random diffusion. We study the transience and recurrence properties and the central limit theorem proper...
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作者：SAMORODNITSKY, G; TAQQU, MS
作者单位：Boston University
摘要：We study the relation between stochastic domination of an infinitely divisible random vector X by another infinitely divisible random vector Y and their corresponding Levy measures. The results are used to derive a Slepian-type inequality for a general class of symmetric infinitely divisible random vectors.
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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：BAI, ZD; YIN, YQ
作者单位：University of Massachusetts System; University of Massachusetts Lowell
摘要：In this paper, the authors show that the smallest (if p less-than-or-equal-to n) or the (p - n + 1)-th smallest (if p > n) eigenvalue of a sample covariance matrix of the form (1/n)XX' tends almost surely to the limit (1 - square-root y)2 as n and p/n --> y is-an-element-of (0, infinity), where X is a p x n matrix with iid entries with mean zero, variance 1 and fourth moment finite. Also, as a by-product, it is shown that the almost sure limit of the largest eigenvalue is (1 + square-root y)2,...
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作者：GRIFFEATH, D
