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Indexed by:期刊论文

Date of Publication:2016-11-16

Journal:COMMUNICATIONS IN STATISTICS-THEORY AND METHODS

Included Journals:SCIE、EI、Scopus

Volume:45

Issue:22

Page Number:6569-6595

ISSN No.:0361-0926

Key Words:Brownian motion; First exit time; Gordon's ineuqality; Regular variation

Abstract:Consider the following domains:
   D-min = {(x, y(1), y(2)) : parallel to x parallel to < min{(y(j) + h(j) + 1)(1/pj), j = 1, 2}}
   D-max = {(x, y(1), y(2)) : parallel to x parallel to < max{(y(j) + h(j) + 1)(1/pj), j = 1, 2}}
   in Rd+2, d >= 1, respectively, where parallel to . parallel to is the Euclidean norm in R-d, and h(j), j = 1, 2, are the regular variations. Let tau(Dmin) and tau(Dmax) be the first time the Brownian motion exits from D-min and D-max, respectively. Estimates for the asymptotics of log P(tau(Dmin) > t) and log P(t(Dmax) > t) are given for t -> 8, depending on the relationship among p(j), and regular variations h(j), j = 1, 2, respectively. The proofs are based on Gordon's inequality.