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论文类型：期刊论文

发表时间：2011-12-01

发表刊物：JOURNAL OF THEORETICAL PROBABILITY

收录刊物：Scopus、SCIE

卷号：24

期号：4

页面范围：1028-1043

ISSN号：0894-9840

关键字：Brownian motion; Bessel process; Gordon's inequality; Exit probabilities

摘要：Consider a Brownian motion starting at an interior point of the minimum or maximum parabolic domains, namely, D(min) = {(x, y(1), y(2)) : ||x|| < min{(y(1) + 1)(1/p1), (y(2) + 1)(1/p2)}} and D(max) = {(x, y(1), y(2)) : ||x|| < max{(y(1) + 1)(1/p1), (y(2) + 1)(1/p2)}} in R(d+2), d >= 1, respectively, where ||.|| is the Euclidean norm in R(d), y(1), y(2) >= -1, and p(1), p(2) > 1. Let iota(Dmin) and iota(Dmax) denote the first times the Brownian motion exits from D(min) and D(max). Estimates with exact constants for the asymptotics of log P(iota(Dmin) > t) and log P(iota(Dmax) > t) are given as t -> infinity, depending on the relationship between p(1) and p(2), respectively. The proof methods are based on Gordon's inequality and early works of Li, Lifshits, and Shi in the single general parabolic domain case.