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作者：LEDRAPPIER, F
摘要：We prove a central limit theorem for the distance of the Brownian point on the universal cover of a compact negatively curved Riemannian manifold. The technical point is a contraction property for the leafwise Brownian motion along the stable foliation.
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作者：LEE, TY
摘要：For a system of infinitely many independent symmetric random walks on Z let K-n(x) be the number of visits to x is an element of Z from time 0 to n - 1. The probabilities of some rare events involving (K-n(0), K-n(1)) are estimated as n-->infinity and the corresponding large deviation rate functions are derived for both deterministic and invariant initial distributions. The dependence on the initial distributions is discussed. A simple method is used for guessing at the rate functions. This me...
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作者：BURDZY, K; TOBY, E
作者单位：Texas A&M University System; Texas A&M University College Station
摘要：We consider two-dimensional reflected Brownian motions in sharp thorns pointed downward with horizontal vectors of reflection. We present a decomposition of the process into a Brownian motion and a process which has bounded variation away from the tip of the thorn. The construction is based on a new Skorohod-type lemma.
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作者：ANTAL, P
摘要：We consider a continuous time simple random walk moving among obstacles, which are sites (resp., bonds) of the lattice Z(d). We derive in this context a version of the technique of enlargement of obstacles developed by Sznitman in the Brownian case. This method gives controls on exponential moments of certain death times as well as good lower bounds for certain principal eigenvalues. We give an application to recover an asymptotic result of Donsker and Varadhan on the number of sites visited b...
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作者：PEMANTLE, R; PERES, Y
作者单位：University of California System; University of California Berkeley
摘要：Evans defined a notion of what it means for a set B to be polar for a process indexed by a tree. The main result herein is that a tree picked from a Galton-Watson measure whose offspring distribution has mean m and finite variance will almost surely have precisely the same polar sets as a deterministic tree of the same growth rate. This implies that deterministic and nondeterministic trees behave identically in a variety of probability models. Mapping subsets of Euclidean space to trees and po...
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作者：HOUDRE, C; PEREZABREU, V
作者单位：CIMAT - Centro de Investigacion en Matematicas
摘要：We present covariance identities and inequalities for functionals of the Wiener and the Poisson processes. Using Malliavin calculus techniques, an expansion with a remainder term is obtained for the covariance of such functionals. Our results extend known identities and inequalities for functions of multivariate random vectors.
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作者：ROSINSKI, J
摘要：Some optimal refinements of the results on strong exponential integrability of sums of independent zero-mean uniformly bounded random vectors are given.
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作者：DARLING, RWR
摘要：Let V-W and V-Y be Euclidean Vector spaces and let V-Z = L(V-W --> V-Y). Given a Wiener process W on V-W, with natural filtration {T-t}, and a T-T-measurable random variable U in V-Y, we seek adapted processes (Y, Z) in V-Y X V-Z satisfying the SDE U = Y(t) + integral((t,T]) ZdW - integral((t,T])Gamma(Y,ZZ*)ds/2, 0 less than or equal to t less than or equal to T, under local Lipschitz and convexity conditions on the map (y, A) --> Gamma(y, A). These conditions apply in particular in the case G...
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作者：LAWLER, GF
摘要：Internal diffusion limited aggregation (internal DLA) is a cluster model in Z(d) where new points are added by starting random walkers at the origin and letting them run until they have found a new point to add to the cluster. It has been shown that the limiting shape of internal DLA. clusters is spherical. Here we show that for d greater than or equal to 2 the fluctuations are subdiffusive; in fact, that they are of order at most n(1/3), at least up to logarithmic corrections. More precisely,...
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作者：XIAO, YM
摘要：The Hausdorff dimension and packing dimension of the image and graph of Gaussian vector fields and index-alpha stable fields are obtained under general conditions which allow for different local behavior of the components and for dependence among them. These results correct some errors in print. The condition for an index-alpha stable field to have k-multiple points are considered and in the case of Nk > (k - 1)Sigma(j=1)(d)alpha(j), the Hausdorff dimension of the set of k-multiple times is gi...
