Electronic Journal of Probability

The Exit Place of Brownian Motion in the Complement of a Horn

Dante DeBlassie

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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.

Article information

Electron. J. Probab., Volume 13 (2008), paper no. 36, 1068-1095.

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60J65: Brownian motion [See also 58J65]

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

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DeBlassie, Dante. The Exit Place of Brownian Motion in the Complement of a Horn. Electron. J. Probab. 13 (2008), paper no. 36, 1068--1095. doi:10.1214/EJP.v13-524. https://projecteuclid.org/euclid.ejp/1464819109

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