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作者：HOUDRE, C
作者单位：University of North Carolina; University of North Carolina Chapel Hill; George Mason University; University System of Maryland; University of Maryland College Park
摘要：The problem of recovering, say, a band-limited weakly stationary process from a set of its irregularly spaced samples is studied. For rather general sampling sequences some sufficient conditions ensuring mean square or pathwise reconstruction are obtained. For the cases of regular samples with either finitely many missing ones and/or finitely many irregular ones, a necessary and sufficient condition is presented. Some elements of the proofs involve classical results on nonharmonic Fourier seri...
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作者：Down, D; Meyn, SP; Tweedie, RL
作者单位：Colorado State University System; Colorado State University Fort Collins
摘要：General characterizations of geometric convergence for Markov chains in discrete time on a general state space have been developed recently in considerable detail. Here we develop a similar theory for phi-irreducible continuous time processes and consider the following types of criteria for geometric convergence: 1. the existence of exponentially bounded hitting times on one and then all suitably ''small'' sets; 2. the existence of ''Foster-Lyapunov'' or ''drift'' conditions for any one and th...
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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...
