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论文类型：期刊论文

发表时间：2014-01-01

发表刊物：COMMUNICATIONS IN STATISTICS-THEORY AND METHODS

收录刊物：SCIE、EI

卷号：43

期号：18

页面范围：3848-3865

ISSN号：0361-0926

关键字：Brownian motion; Exit probabilities; Gordon's inequality; Regular function

摘要：Consider a Brownian motion starting at an interior point of the maximum or minimum domains with regular varying boundary, namely, D-max = {( x, y(1), y(2)) : parallel to x parallel to < max(i=1,2){f(i)(1 + y(i))}} and D-min = {(x, y(1), y(2)) : parallel to x parallel to < min(i=1,2){f(i) (1 + y(i))}}, in Rd+2, d >= 1, respectively, where parallel to.parallel to is the Euclidean norm in R-d, y(1), y(2) >= -1, and f(i) are regularly varying at infinity. Let tau(Dmax) and tau(Dmin) denote the first times the Brownian motion exits from D-max and D-min. Estimates with exact constants for the asymptotics of log P(tau(Dmax) > t) and log P(tau(Dmin) > t) are given as t -> infinity, depending on the relationship between f(1) and f(2), respectively. The proof methods are based on Gordon's inequality and early works of Li, Lifshits, and Shi in the single general domain case.