Stability of Martin boundary under non-local Feynman-Kac perturbations

• 成果类型: Article
• 署名作者: Chen, ZQ; Kim, P
• 署名单位: University of Washington; University of Washington Seattle
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-003-0317-8
• 发表日期: 2004
• 页码: 525-564
• 关键词: censored stable processes; conditional gaugeability; elliptic-equations; harmonic-functions; Transforms; PRINCIPLE; THEOREM; domains; gauge

摘要

Recently the authors showed that the Martin boundary and the minimal Martin boundary for a censored (or resurrected) alpha-stable process Y in a bounded C-1,C-1-open set D with alpha is an element of (1, 2 can all be identified with the Euclidean boundary D of D. Under the gaugeability assumption, we show that the Martin boundary and the minimal Martin boundary for the Schrodinger operator obtained from Y through a non-local Feynman-Kac transform can all be identified with partial derivativeD. In other words, the Martin boundary and the minimal Martin boundary are stable under non-local Feynman-Kac perturbations. Moreover, an integral representation of nonnegative excessive functions for the Schrodinger operator is explicitly given. These results in fact hold for a large class of strong Markov processes, as are illustrated in the last section of this paper. As an application, the Martin boundary for censored relativistic stable processes in bounded C-1,C-1-smooth open sets is studied in detail.