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论文类型：期刊论文

发表时间：2015-05-03

发表刊物：COMMUNICATIONS IN STATISTICS-THEORY AND METHODS

收录刊物：SCIE、EI、Scopus

卷号：44

期号：9

页面范围：1763-1778

ISSN号：0361-0926

关键字：Brownian motion; Bessel process; Regular variation

摘要：Consider a Brownian motion with a regular variation starting at an interior point of a domain D in Rd+1, d >= 1 and let tau(D) denote the first time the Brownian motion exits from D. Estimates with exact constants for the asymptotics of log P(tau(D) > T) are given for T ->infinity, depending on the shape of the domain D and the order of the regular variation. Furthermore, the asymptotically equivalence are obtained. The problem is motivated by the early results of Lifshits and Shi, Li in the first exit time, and Karamata in the regular variation. The methods of proof are based on their results and the calculus of variations.