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April, 1991 Some Potential Theory for Reflecting Brownian Motion in Holder and Lipschitz Domains
Richard F. Bass, Pei Hsu
Ann. Probab. 19(2): 486-508 (April, 1991). DOI: 10.1214/aop/1176990437

Abstract

Bounds are found on the transition densities and Green functions for Brownian motion with normal reflection in Holder and Lipschitz domains. For Lipschitz domains, reflecting Brownian motion and boundary local time are constructed, a Harnack inequality valid up to the boundary is proved, a probabilistic solution to the Neumann problem is given and the Kuramochi boundary is identified.

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Richard F. Bass. Pei Hsu. "Some Potential Theory for Reflecting Brownian Motion in Holder and Lipschitz Domains." Ann. Probab. 19 (2) 486 - 508, April, 1991. https://doi.org/10.1214/aop/1176990437

Information

Published: April, 1991
First available in Project Euclid: 19 April 2007

zbMATH: 0732.60090
MathSciNet: MR1106272
Digital Object Identifier: 10.1214/aop/1176990437

Subjects:
Primary: 60J65
Secondary: 60J35 , 60J50

Keywords: Green function , Holder domain , Kuramochi boundary , Lipschitz domain , Neumann problem , Reflecting Brownian motion , Transition density

Rights: Copyright © 1991 Institute of Mathematical Statistics

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Vol.19 • No. 2 • April, 1991
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