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作者：GANTERT, N
摘要：We prove a local version of Strassen's law of the iterated logarithm. Instead of shrinking larger and larger pieces of a Brownian path and letting time go to infinity, we look at a sequence of functions we get by blowing up smaller and smaller pieces and we investigate the asymptotic behaviour of this sequence as time goes to zero, It turns out that this sequence of functions is a relatively compact subset of C[0, 1] with probability 1, and the set of its limit points is the same as in Strasse...
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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：CHOW, YS; DELAPENA, VH; TEICHER, H
作者单位：Columbia University; Rutgers University System; Rutgers University New Brunswick
摘要：Under suitable conditions on a stopping time T and zero mean i.i.d. random variables (X(n), n greater-than-or-equal-to 1), a Wald-type equation ES(k, T) = 0 is obtained where S(k, n) is the sum of products of k of the X's with indices from 1 to n. This, in turn, is utilized to obtain information about the moments of T(k) = inf{n greater-than-or-equal-to k: S(k, n) greater-than-or-equal-to 0} and W(c) = inf{n greater-than-or-equal-to 2: S1, n2 > cSIGMA(j = 1) X 2(j)2}, C > 0.
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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：BHATT, AG; KARANDIKAR, RL
摘要：We extend Echeverria's criterion for invariant measures for a Markov process characterized via martingale problems to the case where the state space of the Markov process is a complete separable metric space. Essentially, the only additional conditions required are a separability condition on the operator occurring in the martingale problem and the well-posedness of the martingale problem in the class of progressively measurable solutions (as opposed to well-posedness in the class of r.c.l.l. ...
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作者：CSORGO, M; SHAO, QM
作者单位：Zhejiang University
摘要：Based on the well-known Borell inequality and on a general theorem for large and small increments of Banach space valued stochastic processes of Csaki, Csorgo and Shao, we establish some almost sure path behaviour of increments in general, and moduli of continuity in particular, for l(p)-valued, 1 less than or equal to p < infinity, Gaussian processes with stationary increments. Applications to l(p)-valued fractional Wiener and Ornstein-Uhlenbeck processes are also discussed. Our results refin...
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作者：PITTEL, B
摘要：In a set of even cardinality n, each member ranks all the others in order of preference. A stable matching is a partition of the set into n/2 pairs, with the property that no two unpaired members both prefer each other to their partners under matching. It is known that for some problem instances no stable matching exists. What if an instance of the ranking system is chosen uniformly at random? We show that the mean and the variance of the total number of stable matchings for the random problem...
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作者：RIO, E
摘要：Let (X(i))i is-an-element-of Z+d be an array of independent identically distributed zero-mean random vectors with values in R(k). When E(\X1\r) < + infinity, for some r > 2, we obtain the strong approximation of the partial sum process (SIGMA(i is-an-element-of nuS)X(i): S is-an-element-of l) by a Gaussian partial sum process (SIGMA(i is-an-element-of nuS)Y(i): S is-an-element l), uniformly over all sets in a certain Vapnik-Cher-vonenkis class l of subsets of [0, 1]d. The most striking result ...
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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...
