Some Potential Theory for Reflecting Brownian Motion in Holder and Lipschitz Domains
Open Access
- 1 April 1991
- journal article
- Published by Institute of Mathematical Statistics in The Annals of Probability
- Vol. 19 (2) , 486-508
- https://doi.org/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.Keywords
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