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2008 The Exit Place of Brownian Motion in the Complement of a Horn
Dante DeBlassie
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Electron. J. Probab. 13: 1068-1095 (2008). DOI: 10.1214/EJP.v13-524


Consider the domain lying outside a horn. We determine asymptotics of the logarithm of the chance that Brownian motion in the domain has a large exit place. For a certain class of horns, the behavior is given explicitly in terms of the geometry of the domain. We show that for some horns the behavior depends on the dimension, whereas for other horns, it does not. Analytically, the result is equivalent to estimating the harmonic measure of the part of the domain lying outside a cylinder with large diameter.


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Dante DeBlassie. "The Exit Place of Brownian Motion in the Complement of a Horn." Electron. J. Probab. 13 1068 - 1095, 2008.


Accepted: 9 July 2008; Published: 2008
First available in Project Euclid: 1 June 2016

zbMATH: 1190.60076
MathSciNet: MR2424987
Digital Object Identifier: 10.1214/EJP.v13-524

Primary: 60J65

Keywords: $h$-transform , exit place of Brownian motion , Feynman-Kac representation , harmonic measure , Horn-shaped domain

Vol.13 • 2008
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