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March 2009 Transcience/recurrence for normally reflected Brownian motion in unbounded domains
Ross G. Pinsky
Ann. Probab. 37(2): 676-686 (March 2009). DOI: 10.1214/08-AOP416


Let DRd 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)∈Rl+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.


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Ross G. Pinsky. "Transcience/recurrence for normally reflected Brownian motion in unbounded domains." Ann. Probab. 37 (2) 676 - 686, March 2009.


Published: March 2009
First available in Project Euclid: 30 April 2009

zbMATH: 1169.60018
MathSciNet: MR2510020
Digital Object Identifier: 10.1214/08-AOP416

Primary: 60J65

Keywords: Brownian motion , hitting times , Neumann Laplacian , normal reflection , recurrence , transience

Rights: Copyright © 2009 Institute of Mathematical Statistics

Vol.37 • No. 2 • March 2009
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