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作者：DeBlassie, D
作者单位：Texas A&M University System; Texas A&M University College Station
摘要：For continuous gamma, g:[0, 1] --> (0, infinity), consider the degenerate stochastic differential equation dX(t) = [1 - \X-t \(2)](1/2)gamma(\X-t\)dB(t) - g(\X-t\)X-t dt in the closed unit ball of R-n. We introduce a new idea to show pathwise uniqueness holds when gamma and g are Lipschitz and g(1)/gamma(2)(1) > root2 -1 . When specialized to a case studied by Swart [Stochastic Process. Appl. 98 (2002) 131-149] with gamma = root2 and g equivalent to c, this gives an improvement of his result. ...
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作者：Hassairi, A; Zarai, M
作者单位：Universite de Sfax; Faculty of Sciences Sfax
摘要：This paper introduces a notion of 2-orthogonality for a sequence of polynomials to give extended versions of the Meixner and Feinsilver characterization results based on orthogonal polynomials. These new versions subsume the Letac-Mora characterization of the real natural exponential families having cubic variance function.
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作者：Asselah, A; Pra, PD
作者单位：Aix-Marseille Universite; University of Padua
摘要：We consider the symmetric exclusion process {eta(t), t > 0} on {0,1}(Zd). We fix a pattern A := {eta: Sigma(Lambda) eta(i) greater than or equal to k}, where Lambda is a finite subset of Z(d) and k is an integer, and we consider the problem of establishing sharp estimates for tau, the hitting time of A. We present a novel argument based on monotonicity which helps in some cases to obtain sharp tail asymptotics for tau in a simple way. Also, we characterize the trajectories {eta(s), s less than...
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作者：Dalang, RC; Nualart, E
作者单位：Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne
摘要：We give general sufficient conditions which imply upper and lower bounds for the probability that a multiparameter process hits a given set E in terms of a capacity of E related to the process. This extends a result of Khoshnevisan and Shi [Ann. Probab. 27 (1999) 1135-1159], where estimates for the hitting probabilities of the (N, d) Brownian sheet in terms of the (d - 2N) Newtonian capacity are obtained, and readily applies to a wide class of Gaussian processes. Using Malliavin calculus and, ...
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作者：De La Peña, VH; Klass, MJ; Lai, TL
作者单位：Columbia University; University of California System; University of California Berkeley; Stanford University
摘要：Self-normalized processes arise naturally in statistical applications. Being unit free, they are not affected by scale changes. Moreover, self-normalization often eliminates or weakens moment assumptions. In this paper we present several exponential and moment inequalities, particularly those related to laws of the iterated logarithm, for self-normalized random variables including martingales. Tail probability bounds are also derived. For random variables B-t > 0 and A(t), let Y-t(lambda) = ex...
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作者：Manstavicius, M
作者单位：University of Connecticut
摘要：Let xit, t is an element of [0, T], be a strong Markov process with values in a complete separable metric space (X, rho) and with transition probability function P-s,P-t (x, dy), 0 less than or equal to s less than or equal to t less than or equal to T, x is an element of X. For any h is an element of [0, T] and a > 0, consider the function alpha(h,a) = sup{P-s,P-t(x, {y:rho(x,y) greater than or equal to a}):x is an element of X, 0 less than or equal to s less than or equal to t less than or e...
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作者：Lijoi, A; Regazzini, E
作者单位：University of Pavia; University of Pavia
摘要：The Lauricella theory of multiple hypergeometric functions is used to shed some light on certain distributional properties of the mean of a Dirichlet process. This approach leads to several results, which are illustrated here. Among these are a new and more direct procedure for determining the exact form of the distribution of the mean, a correspondence between the distribution of the mean and the parameter of a Dirichlet process, a characterization of the family of Cauchy distributions as the...
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作者：Fleischmann, K; Swart, JM
作者单位：Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics; University of Erlangen Nuremberg
摘要：In a supercritical branching particle system, the trimmed tree consists of those particles which have descendants at all times. We develop this concept in the superprocess setting. For a class of continuous superprocesses with Feller underlying motion on compact spaces, we identify the trimmed tree, which turns out to be a binary splitting particle system with a new underlying motion that is a compensated h-transform of the old one. We show how trimmed trees may be estimated from above by embe...
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作者：Fuhrman, M; Tessitore, G
作者单位：Polytechnic University of Milan; University of Parma
摘要：Solutions of semilinear elliptic differential equations in infinite-dimensional spaces are obtained by means of forward and backward infinite-dimensional stochastic evolution equations. The backward equation is considered on an infinite time horizon and a suitable growth condition replaces the final condition. Elliptic equations are intended in a mild sense, suitable also for applications to optimal control. We finally notice that, due to the lack of smoothing properties, the elliptic partial ...
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作者：Wu, JM
作者单位：University of Illinois System; University of Illinois Urbana-Champaign
摘要：Let X (t) be the symmetric alpha-stable process in R-d (0 < alpha < 2, d greater than or equal to 2). Then let W(f) be the thorn {x is an element of R-d:0 < x(1) < 1, (x(2)(2) +... + x(d)(2))(1)/(2) < f(x(1))} where f : (0, 1) --> (0, 1) is continuous, increasing with f (0(+)) = 0. Recently Burdzy and Kulczycki gave an exact integral condition on f for the existence of a random time s such that X(t) remains in the thorn X(s) + W(f) for all t is an element of [s, s + 1). We extend their theorem...
