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May 2006 Traces of symmetric Markov processes and their characterizations
Zhen-Qing Chen, Masatoshi Fukushima, Jiangang Ying
Ann. Probab. 34(3): 1052-1102 (May 2006). DOI: 10.1214/009117905000000657


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.


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Zhen-Qing Chen. Masatoshi Fukushima. Jiangang Ying. "Traces of symmetric Markov processes and their characterizations." Ann. Probab. 34 (3) 1052 - 1102, May 2006.


Published: May 2006
First available in Project Euclid: 27 June 2006

zbMATH: 1103.60067
MathSciNet: MR2243879
Digital Object Identifier: 10.1214/009117905000000657

Primary: 31C25 , 60J45 , 60J50

Keywords: Dirichlet form , Douglas integral , Energy Functional , energy measure , excursion , Feller measure , martingale additive functional , positive continuous additive functional , Reflected Dirichlet space , Revuz measure , Stochastic analysis , supplementary Feller measure , Symmetric right process , Time change , Trace

Rights: Copyright © 2006 Institute of Mathematical Statistics

Vol.34 • No. 3 • May 2006
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