Transcience/recurrence for normally reflected Brownian motion in unbounded domains

Ross G. Pinsky

doi:10.1214/08-AOP416

Transcience/recurrence for normally reflected Brownian motion in unbounded domains

Probability 2009-06-22 v2 Spectral Theory

Authors: Ross G. Pinsky

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Abstract

Let $D\subsetneq R^d$ 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.

Keywords

brownian motion pseudoconvex domains

Cite

@article{arxiv.0803.3748,
  title  = {Transcience/recurrence for normally reflected Brownian motion in unbounded domains},
  author = {Ross G. Pinsky},
  journal= {arXiv preprint arXiv:0803.3748},
  year   = {2009}
}

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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)

Transcience/recurrence for normally reflected Brownian motion in unbounded domains

Abstract

Keywords

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