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Indexed by:期刊论文

Date of Publication:2015-05-03

Journal:COMMUNICATIONS IN STATISTICS-THEORY AND METHODS

Included Journals:SCIE、EI、Scopus

Volume:44

Issue:9

Page Number:1763-1778

ISSN No.:0361-0926

Key Words:Brownian motion; Bessel process; Regular variation

Abstract: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.