The Annals of Probability

Some Potential Theory for Reflecting Brownian Motion in Holder and Lipschitz Domains

Richard F. Bass and Pei Hsu

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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.

Article information

Source
Ann. Probab., Volume 19, Number 2 (1991), 486-508.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176990437

Digital Object Identifier
doi:10.1214/aop/1176990437

Mathematical Reviews number (MathSciNet)
MR1106272

Zentralblatt MATH identifier
0732.60090

JSTOR
links.jstor.org

Subjects
Primary: 60J65: Brownian motion [See also 58J65]
Secondary: 60J35: Transition functions, generators and resolvents [See also 47D03, 47D07] 60J50: Boundary theory

Keywords
Reflecting Brownian motion Lipschitz domain Holder domain Kuramochi boundary transition density Green function Neumann problem

Citation

Bass, Richard F.; Hsu, Pei. Some Potential Theory for Reflecting Brownian Motion in Holder and Lipschitz Domains. Ann. Probab. 19 (1991), no. 2, 486--508. doi:10.1214/aop/1176990437. https://projecteuclid.org/euclid.aop/1176990437


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