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)∈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.