Traces of symmetric Markov processes and their characterizations

• 成果类型: Article
• 署名作者: Chen, Zhen-Qing; Fukushima, Masatoshi; Ying, Jiangang
• 署名单位: University of Washington; University of Washington Seattle; Kansai University; Fudan University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/009117905000000657
• 发表日期: 2006
• 页码: 1052-1102
• 关键词: censored stable processes; dirichlet forms; time changes

摘要

Time change is one of the most basic and very useful transformations for Markov processes. The time changed process can also be regarded as the trace of the original process on the support of the Revuz measure used in the time change. In this paper we give a complete characterization of time changed processes of an arbitrary symmetric Markov process, in terms of the Beurling-Deny decomposition of their associated Dirichlet forms and of Feller measures of the process. In particular, we determine the jumping and killing measure (or, equivalently, the Levy system) for the time-changed process. We further discuss when the trace Dirichlet form for the time changed process can be characterized as the space of finite Douglas integrals defined by Feller measures. Finally, we give a probabilistic characterization of Feller measures in terms of the excursions of the base process.