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Discontinuous Time Changes and Duality for Markov Processes

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Seminar on Stochastic Processes, 1985

Part of the book series: Progress in Probability and Statistics ((PRPR,volume 12))

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Abstract

The purpose of this paper is to continue work on discontinuous time changes of dual Markov processes begun in [6], where time changes based on discontinuous natural additive functionals were discussed. Both continuous and discontinuous natural time changes share the features

  1. (i)

    dual time changes (i.e., based on dual additive functionals) preserve duality,

  2. (ii)

    the new duality measure of the time changed processes is constructed from the Revuz measure of the time changing additive functionals.

In this paper, we consider the general case of time changes based on additive functionals which have a quasi-left-continuous purely discontinuous component, and present for them a time changing procedure which possesses features (i) and (ii) above.

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References

  1. R. M. Blumenthal and R. K. Getoor. Markov Processes and Potential Theory. Academic Press, New York 1968.

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  3. E. Cinlar and H. Kaspi. Regenerative systems and Markov additive processes. Seminar on Seminar on Stochastic Processes 1982, 123–147. Birkhäuser, Boston, 1983.

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Author information

Authors and Affiliations

  1. Department of Mathematical Sciences, University of Cincinnati, Cincinnati, Ohio, 45221-0025, USA

    Joanna B. Mitro

Authors
  1. Joanna B. Mitro
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Editor information

Editors and Affiliations

  1. Civil Engineering Department, Princeton University, Princeton, NJ, 08544, USA

    E. Çinlar

  2. Department of Mathematics, Stanford University, Stanford, CA, 94305, USA

    K. L. Chung

  3. Department of Mathematics, University of California-San Diego, La Jolla, CA, 92093, USA

    R. K. Getoor

  4. Department of Mathematics, University of Florida, Gainesville, FL, 32611, USA

    J. Glover

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© 1986 Birkhäuser Boston, Inc.

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Mitro, J.B. (1986). Discontinuous Time Changes and Duality for Markov Processes. In: Çinlar, E., Chung, K.L., Getoor, R.K., Glover, J. (eds) Seminar on Stochastic Processes, 1985. Progress in Probability and Statistics, vol 12. Birkhäuser Boston. https://doi.org/10.1007/978-1-4684-6748-2_11

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  • DOI: https://doi.org/10.1007/978-1-4684-6748-2_11

  • Publisher Name: Birkhäuser Boston

  • Print ISBN: 978-1-4684-6750-5

  • Online ISBN: 978-1-4684-6748-2

  • eBook Packages: Springer Book Archive

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