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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 be the Wiener sausage in , that is, the -neighborhood for some of the path of Brownian motion up to time . It is shown that integrals of the type , with nonincreasing and , have a large deviation behavior similar to that of 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 when the traps decay independently with lifetime distribution . There are two critical phenomena: (i) in the exponent of the tail of the survival probability has a crossover at ; (ii) in the survival strategy changes at time , provided , respectively, .