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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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Additive Functionals of Symmetric Markov Processes

Additive Functionals of Symmetric Markov Processes

(p.130) Chapter Four Additive Functionals of Symmetric Markov Processes
Symmetric Markov Processes, Time Change, and Boundary Theory (LMS-35)

Zhen-Qing Chen

Masatoshi Fukushima

Princeton University Press

This chapter is devoted to the study of additive functionals of symmetric Markov processes under the same setting as in the preceding chapter, namely, that E is a locally compact separable metric space, B(E) is the family of all Borel sets of E, and m is a positive Radon measure on E with supp[m] = E, and this chapter considers an m-symmetric Hunt process X = (Ω‎,M,Xₜ,ζ‎,Pₓ) on (E,B(E)) whose Dirichlet form (E,F) on L²(E; m) is regular on L²(E; m). The transition function and the resolvent of X are denoted by {Pₜ; t ≥ 0}, {Rα‎, α‎ > 0}, respectively. B*(E) will denote the family of all universally measurable subsets of E. Any numerical function f defined on E will be always extended to E by setting f(∂) = 0.

Keywords:   additive functionals, symmetric Markov processes, positive continuous additive functionals, smooth measures, decompositions, probabilistic derivation, Beurling-Deny formula

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