Traces of symmetric Markov processes and their characterizations
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Zhen-Qing Chen [1] ; Masatoshi Fukushima [2] ; Jiangang Ying [3]
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[1] University of Washington
University of Washington
Estados Unidos
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[2] Kansai University
Kansai University
Japón
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[3] Fudan University
Fudan University
China
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- Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 34, Nº. 3, 2006, págs. 1052-1102
- Idioma: inglés
- DOI: 10.1214/009117905000000657
- Texto completo no disponible (Saber más ...)
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Resumen
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 Lévy 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.
