Reflected symmetric α-stable processes and regional fractional Laplacian

• 成果类型: Article
• 署名作者: Guan, QY; Ma, ZM
• 署名单位: Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-005-0438-3
• 发表日期: 2006
• 页码: 649-694
• 关键词: boundary harnack principle; intrinsic ultracontractivity; conditional gauge

摘要

In this paper we investigate the reflected symmetric alpha-stable processes and their generators. We show that the generators are regional fractional Laplacians on the closed region. In the case of 1 <= alpha < 2 their existence requires that partial derivative u/partial derivative n = 0 on the boundary. Among other things we obtain the integration by parts formula of the regional fractional Laplacian and the semi-martingale decomposition of the reflected symmetric alpha-stable processes.