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January, 1994 Survival Asymptotics for Brownian Motion in a Poisson Field of Decaying Traps
Erwin Bolthausen, Frank Den Hollander
Ann. Probab. 22(1): 160-176 (January, 1994). DOI: 10.1214/aop/1176988853


Let $W(t)$ be the Wiener sausage in $\mathbb{R}^d$, 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 $\int^t_0\nu(s) d|W(s)|$, with $t \rightarrow \nu (t)$ nonincreasing and $nu (t) \sim \nu t^{-\gamma}, t \rightarrow \infty$, 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 $d \geq 3$ the exponent of the tail of the survival probability has a crossover at $\gamma = 2/d$; (ii) in $d \geq 1$ the survival strategy changes at time $s = \lbrack\gamma/(1 + \gamma)\rbrack t$, provided $\gamma < 1/2, d = 1$, respectively, $\gamma < 2/d, d \geq 2$.


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Erwin Bolthausen. Frank Den Hollander. "Survival Asymptotics for Brownian Motion in a Poisson Field of Decaying Traps." Ann. Probab. 22 (1) 160 - 176, January, 1994.


Published: January, 1994
First available in Project Euclid: 19 April 2007

zbMATH: 0793.60086
MathSciNet: MR1258871
Digital Object Identifier: 10.1214/aop/1176988853

Primary: 60J55
Secondary: 60G17 , 60G57

Keywords: Haudorff dimension , Hoder continuity , join continuity , Local times , Measure-valued processes , path properties , Superprocesses

Rights: Copyright © 1994 Institute of Mathematical Statistics


Vol.22 • No. 1 • January, 1994
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