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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：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：ROSINSKI, J; SAMORODNITSKY, G
作者单位：Cornell University
摘要：Subadditive functionals on the space of sample paths include suprema, integrals of paths, oscillation on sets and many others. In this paper we find an optimal condition which ensures that the distribution of a subadditive functional of sample paths of an infinitely divisible process belongs to the subexponential class of distributions. Further, we give exact tail behavior for the distributions of such functionals, thus improving many recent results obtained for particular forms of subadditive...
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作者：MYKLAND, PA
摘要：The paper contains a ''smoothed'' one-step triangular array asymptotic expansion for discrete-time martingales. An important element of the proof is a second-order description of Skorokhod embedding of discrete martingales in continuous ones. An application to Markov processes is given, along with a bootstrapping example.
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作者：ANDJEL, ED
摘要：Bootstrap percolation is a model in which an element of Z2 becomes occupied in one time unit if two appropriately chosen neighbors are occupied. Schonmann [4] proved that starting from a Bernoulli product measure of positive density, the distribution of the time needed to occupy the origin decays exponentially. We show that for alpha > 1, the exponent can be taken as deltap2alpha for some delta > 0, thus showing that the associated characteristic exponent is at most two. Another characteristic...
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作者：LAHIRI, SN
摘要：Let S(n) denote the nth normalized partial sum of a sequence of mean zero, weakly dependent random vectors. This paper gives asymptotic expansions for Ef(S(n)) under weaker moment conditions than those of Gotze and Hipp (1983). It is also shown that an expansion for Ef(S(n)) with an error term o(n-(s-2)/2) is valid without any Cramer-type condition, if f has partial derivatives of order (s-1) only. This settles a conjecture of Gotze and Hipp in their 1983 paper.
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作者：MAITRA, A; SUDDERTH, W
摘要：We consider two-person zero-sum stochastic games with limit superior payoff function and Borel measurable state and action spaces. The games are shown to have a value and the value function is calculated by transfinite iteration of an operator and proved to be upper analytic. The paper extends results of our earlier article [17] in which the same class of games was considered for countable state spaces and finite action sets.
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作者：KESTEN, H
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作者：ALBEVERIO, S; ROCKNER, M; ZHANG, TS
作者单位：University of Bonn; University of Edinburgh
摘要：A Cameron-Martin-Girsanov-Maruyama type formula for symmetric diffusions on infinite dimensional state space is proved. In particular, relaxations of the usual assumptions which still imply absolute continuity (but possibly no longer equivalence) of the path space measures are discussed. In addition a converse result is proved, that is, we show that absolute continuity of the path space measures enables us to identify the underlying Dirichlet form.
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作者：IMKELLER, P
摘要：Let f be a square-integrable function on the unit square. Assume that the singular numbers (a(i))i is-an-element-of N of the Hilbert-Schmidt operator associated with f admit some 0 < alpha < 1/3 such that SIGMA(i = 1)infinity \alpha(i)\alpha < infinity. We present a purely stochastic method to investigate the occupation densities of the Skorohod integral process U induced by f. It allows us to show that U possesses continuous square-integrable occupation densities and obviously generalizes bey...
