## Electronic Journal of Probability

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

Dante DeBlassie

#### Abstract

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

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

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

https://projecteuclid.org/euclid.ejp/1464819109

Digital Object Identifier
doi:10.1214/EJP.v13-524

Mathematical Reviews number (MathSciNet)
MR2424987

Zentralblatt MATH identifier
1190.60076

Subjects

Rights

#### Citation

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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