SOME POTENTIAL-THEORY FOR REFLECTING BROWNIAN-MOTION IN HOLDER AND LIPSCHITZ-DOMAINS

• 成果类型: Article
• 署名作者: BASS, RF; PEI, H
• 署名单位: Northwestern University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1176990437
• 发表日期: 1991
• 页码: 486-508
• 关键词: boundary-conditions

摘要

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.