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Symmetric Markov Processes, Time Change, and Boundary Theory (LMS-35)$
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Zhen-Qing Chen and Masatoshi Fukushima

Print publication date: 2011

Print ISBN-13: 9780691136059

Published to Princeton Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691136059.001.0001

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Symmetric Hunt Processes and Regular Dirichlet Forms

Symmetric Hunt Processes and Regular Dirichlet Forms

(p.92) Chapter Three Symmetric Hunt Processes and Regular Dirichlet Forms
Symmetric Markov Processes, Time Change, and Boundary Theory (LMS-35)

Zhen-Qing Chen

Masatoshi Fukushima

Princeton University Press

This chapter studies a symmetric Hunt process associated with a regular Dirichlet form. Without loss of generality, the majority of the chapter assumes 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,B(E)) whose Dirichlet form (E,F) is regular on L²(E; m). It adopts without any specific notices those potential theoretic terminologies and notations that are formulated in the previous chapter for the regular Dirichlet form (E,F). Furthermore, throughout this chapter, the convention that any numerical function on E is extended to the one-point compactification E = E ∪ {∂} by setting its value at δ‎ to be zero is adopted.

Keywords:   symmetric Hunt processes, regular Dirichlet forms, analytic concepts, hitting distributions, quasi properties, fine properties, part processes, transience, recurrence, path behavior

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