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Symmetric Markov Processes, Time Change, and Boundary Theory (LMS-35) by Zhenqing Chen, Masatoshi Fukushima

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  Chapter Three

 

SYMMETRIC HUNT PROCESSESAND REGULAR DIRICHLET FORMS

As is clearly embodied by Theorem 1.4.3, three theorems of Section 1.5, and Theorem 3.1.13 below, the study of general symmetric Markov processes can be essentially reduced to the study of a symmetric Hunt process associated with a regular Dirichlet form. So without loss of generality, we assume throughout this chapter, except for the last parts of Sections 3.1 and 3.5, that E is a locally compact separable metric space, m is a positive Radon measure on E with supp[m] = E, and X = (Xt, Px) is an m-symmetric Hunt process on (E, image(E)) whose Dirichlet form (ε, ) is regular on L

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