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论文类型：期刊论文

发表时间：2015-08-03

发表刊物：COMMUNICATIONS IN STATISTICS-THEORY AND METHODS

收录刊物：SCIE、EI、Scopus

卷号：44

期号：15

页面范围：3192-3217

ISSN号：0361-0926

关键字：Asymptotical estimates; Brownian motion; Gordon's inequality

摘要：Consider a Brownian motion with drift starting at an interior point of the minimum or maximum parabolic domains, namely,
   D-min = {(x, y(1), y(2)) : parallel to x parallel to < min(j=1,2) {(y(j) + s(rj) + 1)(1/pj)}},
   D-max = {(x, y(1), y(2)) : parallel to x parallel to < max(j=1,2) {(y(j) + s(rj) + 1)(1/pj)}},
   in Rd+2, d >= 1, respectively, where parallel to . parallel to is the Euclidean norm in R-d. Let tau(Dmin), and tau(Dmax) denote the first times the Brownian motion exits from D-min and D-max. Estimates with exact constants for the asymptotics of logP(tau(Dmin) > t) and logP(tau(Dmax) > t) are given as t -> infinity, depending on the relationship among p(j), r(j), j = 1, 2, respectively. The proofs are based on Gordon's inequality.