Open Access
2009 The Exit Place of Brownian Motion in an Unbounded Domain
Dante DeBlassie
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Electron. J. Probab. 14: 2657-2690 (2009). DOI: 10.1214/EJP.v14-726


For Brownian motion in an unbounded domain we study the influence of the "far away" behavior of the domain on the probability that the modulus of the Brownian motion is large when it exits the domain. Roughly speaking, if the domain expands at a sublinear rate, then the chance of a large exit place decays in a subexponential fashion. The decay rate can be explicitly given in terms of the sublinear expansion rate. Our results encompass and extend some known special cases.


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Dante DeBlassie. "The Exit Place of Brownian Motion in an Unbounded Domain." Electron. J. Probab. 14 2657 - 2690, 2009.


Accepted: 14 December 2009; Published: 2009
First available in Project Euclid: 1 June 2016

zbMATH: 1191.60092
MathSciNet: MR2576755
Digital Object Identifier: 10.1214/EJP.v14-726

Primary: 60J65

Keywords: $h$-transform , exit place of Brownian motion , Green function , harmonic measure , Horn-shaped domain , parabolic-type domain

Vol.14 • 2009
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