Skip to main content

Advertisement

SpringerLink
Log in
Menu
Find a journal Publish with us
Search
Cart
  1. Home
  2. Probability Theory and Related Fields
  3. Article
A discontinuous time change for natural additive functionals which preserves duality
Download PDF
Download PDF
  • Published: June 1986

A discontinuous time change for natural additive functionals which preserves duality

  • Joanna B. Mitro1 

Probability Theory and Related Fields volume 72, pages 463–470 (1986)Cite this article

  • 59 Accesses

  • 1 Citations

  • Metrics details

Summary

Continuous time changes of Markov processes preserve duality, but a discontinuous time change recently proposed by Weidenfeld does not. We modify his procedure to obtain a time change which preserves duality when the time changing functional is natural.

Download to read the full article text

Working on a manuscript?

Avoid the common mistakes

References

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

    Google Scholar 

  2. Getoor, R.K.: Multiplicative functionals of dual processes. Ann. Inst. Fourier (Grenoble) 21, 43–83 (1971)

    Google Scholar 

  3. Getoor, R.K., Sharpe, M.J.: Naturality, standardness, and weak duality for Markov processes. Z. Wahrscheinlichkeitstheor. Verw. Geb. 67, 1–62 (1984)

    Google Scholar 

  4. Glover, J.: Discontinuous time changes of semiregenerative processes and balayage theorems. Z. Wahrscheinlichkeitstheor. Verw. Geb. 65, 145–160 (1983)

    Google Scholar 

  5. Jacod, J.: Semi-groupes et mesures invariantes pour les processus semi-markoviens à espace d'état quelconque. Ann. Inst. H. Poincaré IX, 77–112 (1973)

    Google Scholar 

  6. Mitro, J.B.: A note on discontinuous time changes of Markov processes. (Preprint)

  7. Revuz, D.: Mesures associées aux fonctionelles additives de Markov. I. Trans. Am. Math. Soc. 148, 501–531 (1970)

    Google Scholar 

  8. Revuz, D.: Mesures associées aux fonctionelles additives de Markov. II. Z. Wahrscheinlichkeitstheor. Verw. Geb. 16, 336–344 (1970)

    Google Scholar 

  9. Sharpe, M.J.: Discontinuous additive functionals of dual processes. Z. Wahrscheinlichkeitstheor. Verw. Geb. 21, 81–95 (1972)

    Google Scholar 

  10. Sharpe, M.J.: Exact multiplicative functionals in duality. Indiana Math. J. 21, 27–60 (1971)

    Google Scholar 

  11. Smythe, R.T., Walsh, J.B.: The existence of dual processes. Invent. Math. 10, 57–81 (1970)

    Google Scholar 

  12. Weidenfeld, G.: Changements de temps de processus de Markov. Z. Wahrscheinlichkeitstheor. Verw. Geb. 53, 123–146 (1980)

    Google Scholar 

Download references

Author information

Authors and Affiliations

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

    Joanna B. Mitro

Authors
  1. Joanna B. Mitro
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Research supported in part by a Taft Grant-in-Aid of Research from the Charles Phelps Taft Memorial Fund, University of Cincinnati

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Mitro, J.B. A discontinuous time change for natural additive functionals which preserves duality. Probab. Th. Rel. Fields 72, 463–470 (1986). https://doi.org/10.1007/BF00334196

Download citation

  • Received: 05 August 1985

  • Issue Date: June 1986

  • DOI: https://doi.org/10.1007/BF00334196

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

Keywords

  • Stochastic Process
  • Probability Theory
  • Statistical Theory
  • Markov Process
  • Continuous Time
Download PDF

Working on a manuscript?

Avoid the common mistakes

Advertisement

Search

Navigation

  • Find a journal
  • Publish with us

Discover content

  • Journals A-Z
  • Books A-Z

Publish with us

  • Publish your research
  • Open access publishing

Products and services

  • Our products
  • Librarians
  • Societies
  • Partners and advertisers

Our imprints

  • Springer
  • Nature Portfolio
  • BMC
  • Palgrave Macmillan
  • Apress
  • Your US state privacy rights
  • Accessibility statement
  • Terms and conditions
  • Privacy policy
  • Help and support

167.114.118.210

Not affiliated

Springer Nature

© 2023 Springer Nature