Smooth measures and continuous additive functionals of right Markov processes

P. J. Fitzsimmons and R. K. Getoor
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P. J. Fitzsimmons: University of California, San Diego, Department of Mathematics
R. K. Getoor: University of California, San Diego, Department of Mathematics

A chapter in Itô’s Stochastic Calculus and Probability Theory, 1996, pp 31-49 from Springer

Abstract: Summary The Revuz correspondence sets up a bijection between the class of positive continuous additive functionals of a Markov process and a certain class of “smooth” measures on the state space of the process. We consider the correspondence in the context of a Borel right process with a distinguished excessive measure. A “nest” type characterization of smooth measures is provided, as well as a capacitary characterization of nests. Our results extend work of Revuz, Fukushima, and others.

Keywords: Markov Process; Dirichlet Form; Exit Time; Weak Duality; Strong Equilibrium (search for similar items in EconPapers)
Date: 1996
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DOI: 10.1007/978-4-431-68532-6_3

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