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The uniqueness of symmetrizing measure of Markov processes

Authors: Jiangang Ying and Minzhi Zhao
Journal: Proc. Amer. Math. Soc. 138 (2010), 2181-2185
MSC (2010): Primary 60J45, 60J40
Published electronically: January 28, 2010
MathSciNet review: 2596057
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Abstract | References | Similar Articles | Additional Information

Abstract: In this short article, we shall introduce the notion of fine irreducibility and give some of its equivalent statements. Then we prove that the fine irreducibility implies the uniqueness of symmetrizing measures for a right Markov process.

References [Enhancements On Off] (What's this?)

  • 1. R. M. Blumenthal and R. K. Getoor, Markov processes and potential theory, Pure and Applied Mathematics, Vol. 29, Academic Press, New York-London, 1968. MR 0264757
  • 2. Z. Q. Chen and M. Fukushima, Symmetric Markov Processes, Time Change and Boundary Theory, available at zchen/CF/cfbook-PUP32.pdf.
  • 3. Masatoshi Fukushima, Yōichi Ōshima, and Masayoshi Takeda, Dirichlet forms and symmetric Markov processes, De Gruyter Studies in Mathematics, vol. 19, Walter de Gruyter & Co., Berlin, 1994. MR 1303354
  • 4. Michael Sharpe, General theory of Markov processes, Pure and Applied Mathematics, vol. 133, Academic Press, Inc., Boston, MA, 1988. MR 958914

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Additional Information

Jiangang Ying
Affiliation: Department of Mathematics, Fudan University, Shanghai 200433, People’s Republic of China

Minzhi Zhao
Affiliation: Department of Mathematics, Zhejiang University, Hangzhou 310027, People’s Republic of China

Keywords: Symmetrizing measure, linear diffusion, Dirichlet space, regular subspace
Received by editor(s): July 24, 2009
Received by editor(s) in revised form: September 30, 2009
Published electronically: January 28, 2010
Additional Notes: The research of the first author was supported in part by NSFC Grant No. 10771131
The research of the second author was supported in part by NSFC Grant No. 10601047
Communicated by: Richard C. Bradley
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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