Smooth measures and continuous additive functionals of right Markov processes

  • P. J. Fitzsimmons
  • R. K. Getoor


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.


Markov Process Dirichlet Form Exit Time Weak Duality Strong Equilibrium 
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Copyright information

© Springer-Verlag Tokyo 1996

Authors and Affiliations

  • P. J. Fitzsimmons
    • 1
  • R. K. Getoor
    • 1
  1. 1.Department of MathematicsUniversity of California, San DiegoLa JollaUSA

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