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

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  Chapter Four

ADDITIVE FUNCTIONALS OF SYMMETRIC MARKOV PROCESSES

This chapter is devoted to the study of additive functionals of symmetric Markov processes under the same setting as in the preceding chapter, namely, we let E be a locally compact separable metric space, B(E) be the family of all Borel sets of E, and m be a positive Radon measure on E with supp[m] = E, and we consider an m-symmetric Hunt process X = (Ω, M, Xt, ξ, Px) on (E, B(E)) whose Dirichlet form (ε, 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 ...

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