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Smooth measures and continuous additive functionals of right Markov processes

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Itô’s Stochastic Calculus and Probability Theory

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.

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Authors and Affiliations

  1. Department of Mathematics, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA, 92093-0112, USA

    P. J. Fitzsimmons & R. K. Getoor

Authors
  1. P. J. Fitzsimmons
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  2. R. K. Getoor
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Editor information

Editors and Affiliations

  1. Department of Computer Science, Ritsumeikan University, 525-77, Kusatsu, Shiga, Japan

    Nobuyuki Ikeda (Professor) (Professor)

  2. Department of Mathematics, Graduate School of Science, Kyoto University, 606-01, Kyoto, Japan

    Shinzo Watanabe (Professor) (Professor)

  3. Department of Mathematics, Faculty of Fundamental Engineering, Osaka University, Toyonaka, Osaka, 560, Japan

    Masatoshi Fukushima (Professor) (Professor)

  4. Graduate School of Mathematics, Kyushu University, Fukuoka, 812, Japan

    Hiroshi Kunita (Professor) (Professor)

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© 1996 Springer-Verlag Tokyo

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Fitzsimmons, P.J., Getoor, R.K. (1996). Smooth measures and continuous additive functionals of right Markov processes. In: Ikeda, N., Watanabe, S., Fukushima, M., Kunita, H. (eds) Itô’s Stochastic Calculus and Probability Theory. Springer, Tokyo. https://doi.org/10.1007/978-4-431-68532-6_3

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  • DOI: https://doi.org/10.1007/978-4-431-68532-6_3

  • Publisher Name: Springer, Tokyo

  • Print ISBN: 978-4-431-68534-0

  • Online ISBN: 978-4-431-68532-6

  • eBook Packages: Springer Book Archive

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