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- W4248204082 abstract "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 <italic>E</italic> is a locally compact separable metric space, <italic>B</italic>(<italic>E</italic>) is the family of all Borel sets of <italic>E</italic>, and <italic>m</italic> is a positive Radon measure on <italic>E</italic> with supp[<italic>m</italic>] = <italic>E</italic>, and this chapter considers an <italic>m</italic>-symmetric Hunt process <italic>X</italic> = (Ω,<italic>M</italic>,<italic>X</italic>ₜ,<italic>ζ</italic>,<bold>P</bold>ₓ) on (<italic>E</italic>,<italic>B</italic>(<italic>E</italic>)) whose Dirichlet form (<italic>E</italic>,<italic>F</italic>) on <italic>L</italic>²(<italic>E</italic>; <italic>m</italic>) is regular on <italic>L</italic>²(<italic>E</italic>; <italic>m</italic>). The transition function and the resolvent of <italic>X</italic> are denoted by {<italic>P</italic>ₜ; <italic>t</italic> ≥ 0}, {<italic>R</italic> <sub>α</sub>, α > 0}, respectively. <italic>B</italic>*(<italic>E</italic>) will denote the family of all universally measurable subsets of E. Any numerical function <italic>f</italic> defined on <italic>E</italic> will be always extended to <italic>E</italic> <sub>∂</sub> by setting <italic>f</italic>(∂) = 0." @default.
- W4248204082 created "2022-05-12" @default.
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- W4248204082 date "2011-11-20" @default.
- W4248204082 modified "2023-09-25" @default.
- W4248204082 title "Additive Functionals of Symmetric Markov Processes" @default.
- W4248204082 doi "https://doi.org/10.23943/princeton/9780691136059.003.0004" @default.
- W4248204082 hasPublicationYear "2011" @default.
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