## 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
Full Text:

### References:

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