Survival asymptotics for Brownian motion in a Poisson field of decaying traps

Permanent URL to this publication: http://dx.doi.org/10.5167/uzh-22620

Bolthausen, E; den Hollander, F (1994). Survival asymptotics for Brownian motion in a Poisson field of decaying traps. The Annals of Probability, 22(1):160-176.

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Abstract

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, $\gamma < 2/d, d \geq 2$ .

Item Type:	Journal Article, refereed, original work
Communities & Collections:	07 Faculty of Science > Institute of Mathematics
DDC:	510 Mathematics
Uncontrolled Keywords:	Superprocesses; measure-valued processes; local times; join continuity; Hoder continuity; path properties; Haudorff dimension
Language:	English
Date:	1994
Deposited On:	20 May 2010 17:03
Last Modified:	23 Nov 2012 15:06
Publisher:	Institute of Mathematical Statistics
ISSN:	0091-1798
Publisher DOI:	10.1214/aop/1176988853
Related URLs:	http://www.ams.org/mathscinet-getitem?mr=1258871 http://www.zentralblatt-math.org/zmath/en/search/?q=an:0793.60086

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