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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; Technion Israel Institute of Technology
摘要：Necessary and sufficient conditions are obtained for the almost sure joint continuity of the local time of a strongly symmetric standard Markov process X. Necessary and sufficient conditions are also obtained for the almost sure global boundedness and unboundedness of the local time and for the almost sure continuity, boundedness and unboundedness of the local time in the neighborhood of a point in the state space. The conditions are given in terms of the 1-potential density of X. The proofs r...
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作者：PEMANTLE, R
作者单位：Cornell University
摘要：The contact process on an infinite homogeneous tree is shown to exhibit at least two phase transitions as the infection parameter lambda is varied. For small values of lambda a single infection eventually dies out. For larger lambda the infection lives forever with positive probability but eventually leaves any finite set. (The survival probability is a continuous function of lambda, and the proof of this is much easier than it is for the contact process on d-dimensional integer lattices.) For...
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作者：THOMASSEN, C
摘要：The two-dimensional grid Z2 and any graph of smaller growth rate is recurrent. We show that any graph satisfying an isoperimetric inequality only slightly stronger than that of Z2 is transient. More precisely, if f(k) denotes the smallest number of vertices in the boundary of a connected subgraph with k vertices, then the graph is transient if the infinite sum SIGMA-f(k)-2 converges. This can be applied to parabolicity versus hyperbolicity of surfaces.
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作者：EVANS, SN
摘要：We consider a class of stochastic processes of a type that was first introduced by Dubins and Freedman. These processes are indexed by the lines of descent through an infinite tree and take values in a space of sequences. Our main results concern necessary and sufficient conditions of a potential theoretic type for a subset of the state-space to be hit with positive probability by the sample paths of the process. We examine these conditions in some specific examples and also relate them to con...
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作者：CHEN, HN
摘要：In this paper we study a growth model known as the contact process with sexual reproduction on Z2. We focus on the symmetric model in which a child particle can be produced at a vacant site whenever a pair of its neighboring sites is occupied by parent particles. Two kinds of stability of the absorbing state-phi (i,e., the state in which all the sites are vacant) are investigated in this paper. The first kind of stability concerns the behavior of the system when it starts close to the state-ph...
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作者：HENZE, N; VOIGT, B
摘要：Let X(j)(i), i = 1,..., k; j is-an-element-of N, be independent d-dimensional random vectors which are identically distributed for each fixed i = 1,..., k. We give a sufficient condition for almost sure convergence of a sequence T(n1,...,n(k)) of statistics based on X(j)(i) i = 1,....k; j = 1,...,n(i), which are symmetric functions of X1(i),...,X(n(i))(i) for each i and do not change too much when variables are added or deleted. A key auxiliary tool for proofs is the Efron-Stein inequality. Ap...
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作者：FITZSIMMONS, PJ; KANDA, M
作者单位：University of Tsukuba
摘要：Following Choquet, the capacity associated with a Markov process is said to be dichotomous if each compact set K contains two disjoint sets with the same capacity as K. In the context of right processes, we prove that the dichotomy of capacity is equivalent to Hunt's hypothesis that semipolar sets are polar. We also show that a weaker form of the dichotomy is valid for any Levy process with absolutely continuous potential kernel.
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作者：HAHN, MG; WEINER, DC
作者单位：Boston University
摘要：Let {X(j)} be independent, identically distributed random variables with continuous nondegenerate distribution F which is symmetric about the origin. Let {X(n)(1), X(n)(2), . . . , X(n)(n)} denote the arrangement of {X1, . . ., X(n)} in decreasing order of magnitude, so that with probability 1, \X(n)(1)\ > \X(n)(2)\ > ... > \X(n)(n)\. For integers r(n) --> infinity such that r(n)/n --> 0, define the self-normalized trimmed sum T(n) = SIGMA(i = r(n))nX(n)(i)/{SIGMA(i = r(n))nX(n)2(i)}1/2. The a...
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作者：BOUGEROL, P; PICARD, N
作者单位：Universite de Lorraine
摘要：In this paper we consider the multivariate equation X(n+1) = A(n+1)X(n) + B(n+1) with i.i.d. coefficients which have only a logarithmic moment. We give a necessary and sufficient condition for existence of a strictly stationary solution independent of the future. As an application we characterize the multivariate ARMA equations with general noise which have such a solution.
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作者：DELAPENA, VH
摘要：In this paper we introduce a fairly general decoupling inequality for U-statistics. Let {X(i)} be a sequence of independent random variables in a measurable space (S, F), and let (X(i)} be an independent copy of {X(i)}. Let PHI(x) be any convex increasing function for x greater-than-or-equal-to 0. Let PI(ij) be families of functions of two variables taking (S x S) into a Banach space (D, parallel-to . parallel-to). If the f(ij) is-an-element-of PI(ij) are Bochner integrable and [GRAPHICS] then...
