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作者：Aspandilarov, S; Iasnogorodski, R; Menshikov, M
作者单位：Universite de Orleans; Lomonosov Moscow State University
摘要：In this paper we get some sufficient conditions for the finiteness or nonfiniteness of the passage-time moments for nonnegative discrete parameter processes. The developed criteria are closely connected with the well-known results of Foster for the ergodicity of Markov chains and are given in terms of sub(super)martingales. Then, as an application of the obtained results, we get explicit conditions for the finiteness or nonfiniteness of passage-time moments for reflected random walks in a quad...
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作者：Talagrand, M
作者单位：University System of Ohio; Ohio State University
摘要：The concentration of measure phenomenon in product spaces is a far-reaching abstract generalization of the classical exponential inequalities for sums of independent random variables. We attempt to explain in the simplest possible terms the basic concepts underlying this phenomenon, the basic method to prove concentration inequalities and the meaning of several of the most useful inequalities.
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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)
摘要：Let X be an exponentially killed Levy process on T-n, the n-dimensional torus, that satisfies a sector condition. (This includes symmetric Levy processes.) Let F-e denote the extended Dirichlet space of X. Let h is an element of F-e and let {h(y), y is an element of T-n} denote the set of translates of h. That is, h(y)(.) = h(. - y). We consider the family of zero-energy continuous additive functions {N-t([hy]), (y, t) is an element of T-n x R(+)} as defined by Fukushima. For a very large clas...
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作者：Zhang, CH
摘要：Let X, X(n), n greater than or equal to 1, be a sequence of independent identically distributed random variables. We give necessary and sufficient conditions for the strong law of large numbers for k = 2 without regularity conditions on X, [GRAPHICS] for k greater than or equal to 3 in three cases: (i) symmetric X, (ii) P{X greater than or equal to 0} = 1 and (iii) regularly varying P{\X\ > x} as x --> infinity, without further conditions, and for general X and k under a condition on the growt...
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作者：ArenalGutierrez, E; Matran, C
摘要：We develop a new technique to prove the conditional CLT for the weighted bootstrap mean. Through 0-1 laws, we show that this conditional CLT can be derived from an unconditional one which easily arises (conditioning with respect to the weights) from the standard Lindeberg CLT.
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作者：Deheuvels, P; Einmahl, JHJ
作者单位：Eindhoven University of Technology
摘要：We prove functional laws of the iterated logarithm for empirical processes based upon censored data in the neighborhood of a fixed point. We apply these results to obtain strong laws for estimators of local functionals of the lifetime distribution. In particular, we describe the pointwise strong limiting behavior of the kernel density estimator based upon the Kaplan-Meier product-limit estimator.
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作者：Horvath, L; Shao, QM
作者单位：National University of Singapore
摘要：Let {X(n), 1 less than or equal to n < infinity} be a sequence of independent identically distributed random variables in the domain of attraction of a stable law with index 0 < alpha < 2. The limit of x(n)(-1) log P{S-n/max \X(i)\ greater than or equal to x(n)} is found when x(n) --> infinity and x(n)/n --> 0. The large deviation result is used to prove the law of the iterated logarithm for the self-normalized partial sums.
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作者：Kallianpur, G; Xiong, J
作者单位：University of Tennessee System; University of Tennessee Knoxville
摘要：We consider the random fields X(epsilon)(t, q), t greater than or equal to 0, q is an element of O, governed by stochastic partial differential equations driven by a Gaussian white noise in space-time, where O is a bounded domain in R(d) with regular boundary. To study the continuity of the random fields X(epsilon) in space and time variables, we prove an analogue of Garsia's theorem. We then derive the large deviation results based on the methods used by the second author in another paper. Th...
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作者：Jakubowski, A
摘要：We generalize existing Limit theory for stochastic integrals driven by semimartingales and with left-continuous integrands. Joint Skorohod convergence is replaced with joint finite dimensional convergence plus an assumption excluding the case when oscillations of the integrand appear immediately before oscillations of the integrator. Integrands may converge in a very weak topology It is also proved that convergence of integrators implies convergence of stochastic integrals with respect to the ...
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作者：Sethuraman, S; Xu, L
作者单位：Rutgers University System; Rutgers University New Brunswick
摘要：We give easily verifiable conditions under which a functional central limit theorem holds for additive functionals of symmetric simple exclusion and symmetric zero-range processes. Also a reversible exclusion model with speed change is considered. Let eta(t) be the configuration of the process at time t and let f(eta) be a function on the state space. The question is: For which functions f does lambda(-1/2)integral(0)(M) f(eta(s)) ds converge to a Brownian motion? A general but often intractab...
