Release Time:2019-03-09  Hits:

Indexed by: Journal Article

Date of Publication: 2015-08-03

Journal: COMMUNICATIONS IN STATISTICS-THEORY AND METHODS

Included Journals: Scopus、EI、SCIE

Volume: 44

Issue: 15

Page Number: 3192-3217

ISSN: 0361-0926

Key Words: Asymptotical estimates; Brownian motion; Gordon's inequality

Abstract: Consider a Brownian motion with drift starting at an interior point of the minimum or maximum parabolic domains, namely,
   D-min = {(x, y(1), y(2)) : parallel to x parallel to < min(j=1,2) {(y(j) + s(rj) + 1)(1/pj)}},
   D-max = {(x, y(1), y(2)) : parallel to x parallel to < max(j=1,2) {(y(j) + s(rj) + 1)(1/pj)}},
   in Rd+2, d >= 1, respectively, where parallel to . parallel to is the Euclidean norm in R-d. Let tau(Dmin), and tau(Dmax) denote the first times the Brownian motion exits from D-min and D-max. Estimates with exact constants for the asymptotics of logP(tau(Dmin) > t) and logP(tau(Dmax) > t) are given as t -> infinity, depending on the relationship among p(j), r(j), j = 1, 2, respectively. The proofs are based on Gordon's inequality.