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August 2004 Iterated Brownian motion in an open set
R. Dante DeBlassie
Ann. Appl. Probab. 14(3): 1529-1558 (August 2004). DOI: 10.1214/105051604000000404


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 $\frac{1}{8}\Delta^{2}-\frac{\partial}{\partial t}$.


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R. Dante DeBlassie. "Iterated Brownian motion in an open set." Ann. Appl. Probab. 14 (3) 1529 - 1558, August 2004.


Published: August 2004
First available in Project Euclid: 13 July 2004

zbMATH: 1051.60082
MathSciNet: MR2071433
Digital Object Identifier: 10.1214/105051604000000404

Primary: 60J65 , 60K99

Keywords: Exit time , iterated Brownian motion

Rights: Copyright © 2004 Institute of Mathematical Statistics


Vol.14 • No. 3 • August 2004
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