SURVIVAL ASYMPTOTICS FOR BROWNIAN-MOTION IN A POISSON FIELD OF DECAYING TRAPS

• 成果类型: Article
• 署名作者: BOLTHAUSEN, E; DENHOLLANDER, F
• 署名单位: Utrecht University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1176988853
• 发表日期: 1994
• 页码: 160-176
• 关键词: wiener sausage

摘要

Let W(t) be the Wiener sausage in R(d), that is, the a-neighborhood for some a > 0 of the path of Brownian motion up to time t. It is shown that integrals of the type integral0(t)nu(s)d\W(s)\, with t --> nu(t) nonincreasing and nu(t) approximately nut(-gamma), t --> infinity, have a large deviation behavior similar to that of \W(t)\established by Donsker and Varadhan. Such a result gives information about the survival asymptotics for Brownian motion in a Poisson field of spherical traps of radius a when the traps decay independently with lifetime distribution nu(t)/nu(0). There are two critical phenomena: (i) in d greater-than-or-equal-to 3 the exponent of the tail of the survival probability has a crossover at gamma = 2/d; (ii) in d greater-than-or-equal-to 1 the survival strategy changes at time s = [gamma/(1 + gamma)]t, provided gamma < 1/2, d = 1, respectively, gamma < 2/d, d greater-than-or-equal-to 2.