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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

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

Zhen-Qing Chen

Masatoshi Fukushima

Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691136059.003.0004

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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