Iterated Brownian motion in an open set
Open Access
- 1 August 2004
- journal article
- Published by Institute of Mathematical Statistics in The Annals of Applied Probability
- Vol. 14 (3), 1529-1558
- https://doi.org/10.1214/105051604000000404
Abstract
Suppose a solid has a crack filled with a gas. If the crack reaches the surrounding medium, how long does it take the gas to diffuse out of the crack? Iterated Brownian motion serves as a model for diffusion in a crack. If τ is the first exit time of iterated Brownian motion from the solid, then P(τ>t) can be viewed as a measurement of the amount of contaminant left in the crack at time t. We determine the large time asymptotics of P(τ>t) for both bounded and unbounded sets. We also discuss a strange connection between iterated Brownian motion and the parabolic operator .This publication has 42 references indexed in Scilit:
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