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 Electronic Journal of Probability > Vol. 14 (2009) > Paper 93 open journal systems 


The exit place of Brownian motion in an unbounded domain

Dante DeBlassie, New Mexico State University


Abstract
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.


Full text: PDF

Pages: 2657-2690

Published on: December 14, 2009
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Electronic Journal of Probability. ISSN: 1083-6489