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Transcience/recurrence for normally reflected Brownian motion in unbounded domains. (English) Zbl 1169.60018

Author’s abstract: “Let \(D\varsubsetneq \mathbb{R}^d\) be an unbounded domain and let \(B(t)\) be a Brownian motion in \(D\) with normal reflection at the boundary. We study the transience/recurrence dichotomy, focusing mainly on domains of the form \(D=\{(x,z)\in \mathbb{R}^{l+m}:|z|<H(|x|)\},\) where \(d=l+m\) and \(H\) is a sufficiently regular function. This class of domains includes various horn-shaped domains and generalized slab domains.”

MSC:

60J65 Brownian motion
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