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作者：KEENER, RW
摘要：Let {S(n)} be a random walk on the integers with negative drift, and let A(n) = {S(k) greater-than-or-equal-to 0, 1 less-than-or-equal-to k less-than-or-equal-to n} and A = A(infinity). Conditioning on A is troublesome because P(A) = 0 and there is no natural sigma-field of events like A. A natural definition of P(B\A) is lim(n --> infinity) P(B\A(n)). The main result here shows that this definition makes sense, at least for a large class of events B: The finite-dimensional conditional distrib...
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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：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：DYNKIN, EB
摘要：We establish connections between superdiffusion processes and one class of nonlinear parabolic differential equations. Analytic results due to Brezis and Friedman, Baras and Pierre and others are used to investigate the graphs of superdiffusions. A survey of the literature and general comments are presented in Section 4.
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作者：KHOSHNEVISAN, D
作者单位：Massachusetts Institute of Technology (MIT)
摘要：We briefly show an extension of inequalities of Burkholder and Gundy for linear Brownian motion to certain monotone functionals of the d-dimensional Brownian convex hull. Our results belong to a class of results that imply that Brownian hulls are much like the one-dimensional maximal process.
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作者：LIGGETT, TM
摘要：Consider the inhomogeneous contact process on Z1 with recovery rate delta(k) at site k and infection rates lambda(k) and rho(k) at site k due to the presence of infected neighbors at k - 1 and k + 1 respectively. A special case of the main result in this paper is the following: Suppose that the environment is chosen in such a way that the delta(k)'s, lambda(k)'s and rho(k)'s are all mutually independent, with the delta(k)'s having a common distribution, and the lambda(k)'s and rho(k)'s having ...
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作者：DALANG, RC; WALSH, JB
作者单位：University of British Columbia
摘要：This paper examines the question of when a two-parameter process X of independent increments will have Levy's sharp Markov property relative to a given domain D. This property states intuitively that the values of the process inside D and outside D are conditionally independent given the values of the process on the boundary of D. Under mild assumptions, X is the sum of a continuous Gaussian process and an independent jump process. We show that if X satisfies Levy's sharp Markov property, so d...
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作者：ASMUSSEN, S
摘要：The distributions of random walk quantities like ascending ladder heights and the maximum are shown to be phase-type provided that the generic random walk increment X has difference structure X = U - T with U phase-type, or the one-sided assumption of X+ being phase-type is imposed. As a corollary, it follows that the stationary waiting time in a GI/PH/1 queue with phase-type service times is again phase-type. The phase-type representations are characterized in terms of the intensity matrix Q ...
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作者：PEDDADA, SD
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作者：JUREK, ZJ
作者单位：University of Wroclaw
摘要：A notion of U-exponents of a probability measure on a linear space is introduced. These are bounded linear operators and it is shown that the set of all U-exponents forms a Lie wedge for full measures on finite-dimensional spaces. This allows the construction of U-exponents commuting with the symmetry group of a measure in question. Then the set of all commuting exponents is described and elliptically symmetric measures are characterized in terms of their Fourier transforms. Also, self-decompo...
