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Let $D\subsetneq R^d$ be an unbounded domain and let $B(t)$ be a Brownianmotion in $D$ with normal reflection at the boundary. We study thetranscience/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 sufficientlyregular function. This class of domains includes various horn-shaped domainsand generalized slab domains.

Transcience/recurrence for normally reflected Brownian motion in unbounded domains