Transcience/recurrence for normally reflected Brownian motion in unbounded domains

Abstract

Let $D⊊R^d$ be an unbounded domain and let $B(t)$ be a Brownian motion in $D$ with normal reflection at the boundary. We study the transcience/recurrence dichotomy, focusing mainly on domains of the form $D=\{(x,z)\in R^{l+m}:|z|<H(|x|)\}$, where $d=l+m$ and $H$ is a sufficiently regular function. This class of domains includes various horn-shaped domains and generalized slab domains.

Published in at http://dx.doi.org/10.1214/08-AOP416 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)