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.
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