Permanent URL to this publication: http://dx.doi.org/10.5167/uzh22620
Bolthausen, E; den Hollander, F (1994). Survival asymptotics for Brownian motion in a Poisson field of decaying traps. The Annals of Probability, 22(1):160176.

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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 $\int^t_0\nu(s) dW(s)$, 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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Additional indexing
Item Type:  Journal Article, refereed, original work 

Communities & Collections:  07 Faculty of Science > Institute of Mathematics 
Dewey Decimal Classification:  510 Mathematics 
Uncontrolled Keywords:  Superprocesses; measurevalued processes; local times; join continuity; Hoder continuity; path properties; Haudorff dimension 
Language:  English 
Date:  1994 
Deposited On:  20 May 2010 15:03 
Last Modified:  27 Nov 2013 18:16 
Publisher:  Institute of Mathematical Statistics 
ISSN:  00911798 
Publisher DOI:  10.1214/aop/1176988853 
Related URLs:  http://www.ams.org/mathscinetgetitem?mr=1258871 http://www.zentralblattmath.org/zmath/en/search/?q=an:0793.60086 
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