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Indexed by:期刊论文

Date of Publication:2009-10-15

Journal:STATISTICS & PROBABILITY LETTERS

Included Journals:SCIE、Scopus

Volume:79

Issue:20

Page Number:2115-2123

ISSN No.:0167-7152

Abstract:Consider two exit probabilities of the Bessel process |B(s)|
   P(|B(s)| <= min(i=1,2){h(i)(-1) (h(i)(0) + 1 + W(i)(s))}, 0 <= s <= t),
   P(|B(s)| <= min(j=1,2){h(j)(-1) (h(j)(0) + 1 + W(j)(s))}, 0 <= s <= t),
   where h(i)(x), i = 1, 2 are reversible nondecreasing lower semi-continuous convex functions on [0, infinity) with h(i)(0), i = 1, 2 finite. W(1)(s) are independent standard Brownian motions and independent of {B(s) is an element of R(d), t >= 0}. Based on the specific relationship between h(1)(-1) (x) and h(2)(-1) (x), very useful estimates for the asymptotics of log P(.) are given by using Gaussian technique, respectively. (C) 2009 Elsevier B.V. All rights reserved.