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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：CUTLAND, N; NG, SA
摘要：The Loeb measure construction of nonstandard analysis is used to define uniform probability mu(L) on the infinite-dimensional sphere of Poincare, Wiener and Levy, and we construct Wiener measure from it, thus giving rigorous sense to the informal discussion by McKean. From this follows an elementary proof of a weak convergence result. The relation to the infinite product of Gaussian measures is studied. We investigate transformations of the sphere induced by shifts and the associated transform...
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作者：HE, YJ
摘要：A class of topological semigroups called GZH-semigroups is introduced. Conditions under which they have the property that limits of infinitesimal arrays are infinitely divisible are obtained. The convolution semigroup of all probability measures on a second countable LCA-group or on a real separable Hilbert space as well as the semigroup of all positive definite kernels defined on a countable set with complex values and with norms not greater than 1 are reduced to an extended form of Delphic s...
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作者：SKALA, HJ
摘要：In an important paper, Strassen discussed the existence of measures on product spaces with given marginals in the context of Polish spaces. We generalize his results to arbitrary Hausdorff spaces and indicate some applications such as measures with given support and stochastic inequalities on partially ordered Hausdorff spaces, In the second part of our paper, we state two results on the general moment problem, thus generalizing earlier theorems due to Kemperman.
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作者：HAIMAN, G; PURI, ML
作者单位：Indiana University System; Indiana University Bloomington
摘要：It is shown that in the case of stationary Gaussian processes, the Jth (J greater-than-or-equal-to 1) record times {T(n), n greater-than-or-equal-to 1} and the corresponding J-upper order statistics {X(Tn-J+1,Tn),...,X(Tn,Tn)} can almost surely be identified via a translation of the time index n to the corresponding elements defined on a sequence of independent and identically distributed random variables. A construction method for approximating sequences of record times and the corresponding ...
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作者：ENCHEV, O; STROOCK, DW
作者单位：Massachusetts Institute of Technology (MIT)
摘要：Given an R-valued, Borel measurable function F on an abstract Wiener space (E, H, mu), we show that F is uniformly Lipschitz continuous in the directions of H if and only if it has one derivative in the sense of Malliavin and that derivative is an element of L(infinity)(mu; H).
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作者：DUPUIS, P; ISHII, H
作者单位：University of Massachusetts System; University of Massachusetts Amherst; Chuo University
摘要：In this paper we consider stochastic differential equations with reflecting boundary conditions for domains that might have corners and for which the allowed directions of reflection at a point on the boundary of the domain are possibly oblique. The main results are strong existence and uniqueness for solutions of such equations. A key ingredient is a family of relatively regular functions appropriate to the given domain and directions of reflection. Two cases are treated in the paper. In the ...
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作者：REVESZ, P
摘要：Let r(n) be the radius of the largest disc covered by S(1),...,S(n), where (S(k); k = 1, 2,...} is the simple symmetric random walk on Z2. The main result tells us that r(n) greater-than-or-equal-to n1/50 a.s. for all but finitely many n.
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作者：ALDOUS, D
摘要：Let (R(k), k greater-than-or-equal-to 1) be random trees with k leaves, satisfying a consistency condition: Removing a random leaf from R(k) gives R(k - 1). Then under an extra condition, this family determines a random continuum tree l, which it is convenient to represent as a random subset of l1. This leads to an abstract notion of convergence in distribution, as n --> infinity, of (rescaled) random trees T(n) on n vertices to a limit continuum random tree l. The notion is based upon the ass...
