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
Structural properties of randomized times
Download PDF
Download PDF
  • Published: June 1986

Structural properties of randomized times

  • A. F. Karr1 &
  • A. O. Pittenger2 

Probability Theory and Related Fields volume 72, pages 395–415 (1986)Cite this article

  • 54 Accesses

  • Metrics details

Summary

Suppose a measure μ dominates a measure ŋ in the ordering induced by the excessive functions of a transient Markov process. Rost shows than ŋ can be represented as the distribution of the process stopped at a randomized optional time and started with initial distribution μ. In this paper we introduce the shift operator to the class of randomized optional times, inducing the class of randomized quasi-terminal times and that of randomized terminal times. We analyze the algebraic properties of these classes and obtain some compactness results for the class of randomized quasi-terminal times. Some applications, including remplissage by hitting times, are presented.

Download to read the full article text

Working on a manuscript?

Avoid the common mistakes

References

  1. Azéma, J.: Representation multiplicative d'une surmartingale bornée. Z. Wahrscheinlichkeitstheor. Verw. Geb. 45, 191–211 (1978)

    Google Scholar 

  2. Azéma, J., Meyer, P.-A.: Une nouvelle representation du type de Skorokhod. Séminaire de Probabilités VIII, Lecture Notes in Math., vol. 381, 1–10. Berlin Heidelberg New York: Springer 1974

    Google Scholar 

  3. Baxter, J.R., Chacon, R.V.: Compactness of stopping times. Z. Wahrscheinlichkeitstheor. Verw. Geb. 40, 169–181 (1977)

    Google Scholar 

  4. Çinlar, E., Jacod, J., Protter, P. Sharpe, M.J.: Semi-martingales and Markov processes. Z. Wahrscheinlichkeitstheor. Verw. Geb. 54, 161–219 (1980)

    Google Scholar 

  5. Falkner, N.: Embedding in Brownian motion. Ph.D. thesis, University of British Columbia, September 1978

  6. Falkner, N.: On Skorokhod embedding in n-dimensional Brownian motion by means of natural stopping times. Strasbourg Seminaire de Probabilités XIV, Lecture Notes in Math., vol. 784 Berlin Heidelberg New York: Springer 1980

    Google Scholar 

  7. Falkner, N.: Hmbedding processes in Brownian motion in IR n. Trans. AMS 267 335–363 (1981)

    Google Scholar 

  8. Heath, D.: Skorokhod stopping in discrete time. Strasbourg Seminaire de Probabilités IX, Lecture Notes in Math., vol. 465, 515–517. Berlin Heidelberg New York: Springer 1975

    Google Scholar 

  9. Karr, A.F., Pittenger, A.O.: The inverse balayage problem for Markov chains. Stoch. Processes Appl. 7, 165–178 (1978)

    Google Scholar 

  10. Karr, A.F., Pittenger, A.O.: The inverse balayage problem for Markov chains, part II. Stochastic Processes Appl. 9, 35–53 (1979)

    Google Scholar 

  11. Karr, A.F., Pittenger, A.O.: An inverse balayage problem for Brownian motion. Ann. Probab. 7, 186–191 (1979)

    Google Scholar 

  12. Meyer, P.A.: Travaux de H. Rost en théorie du balayage. Strasbourg Seminaire de Probabilités VI, Lecture Notes in Math., vol. 191, 237–250. Berlin Heidelberg New York: Springer 1971

    Google Scholar 

  13. Meyer, P.A.: Cohvergence faible et compacité des temps d'arret d'apres Baxter et Chacon. Strasbourg Seminaire de Probabilités XII, Lecture Notes in Math., vol. 649, 411–423. Berlin Heidelberg New York: Springer 1977

    Google Scholar 

  14. Rost, H.: Die Stoppverteilungen eines Markoff-Prozesses mit lokalendlichem Potential. Manuscripta Math. 3, 321–330 (1970)

    Google Scholar 

  15. Rost, H.: Markov-Ketten bei sich füllenden Löchern im Zustandsraum. Ann. Inst. Fourier 21, 253–270 (1971)

    Google Scholar 

  16. Rost, H.: The stopping distribution of a Markov process. Invent. Math. 14, 1–16 (1971)

    Google Scholar 

  17. Walsh, J.B.: Some topologies connected with Lebesgue measure, Strasbourg Seminaire de Probabilités V, Lecture Notes in Math., vol. 191 290–310. Berlin Heidelberg New York: Springer 1971

    Google Scholar 

  18. Watanabe, T.: Balayées of excessive measures and functions with respect to resolvents, Strasbourg Seminaire de Probabilités V, Lecture Notes in Math., vol. 191 319–341. Berlin Heidelberg New York: Springer 1971

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematical Sciences, The Johns Hopkins University, 21218, Baltimore, MD, USA

    A. F. Karr

  2. Department of Mathematics, University of Maryland Baltimore County, 21228, Baltimore, MD, USA

    A. O. Pittenger

Authors
  1. A. F. Karr
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. O. Pittenger
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Research supported in part by Air Force Office of Scientific Research grant AFOSR 82-0029B

Research supported in part by NSF grant MCS-8404539

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Karr, A.F., Pittenger, A.O. Structural properties of randomized times. Probab. Th. Rel. Fields 72, 395–415 (1986). https://doi.org/10.1007/BF00334193

Download citation

  • Received: 10 April 1985

  • Issue Date: June 1986

  • DOI: https://doi.org/10.1007/BF00334193

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
  • Structural Property
  • Probability Theory
  • Statistical Theory
  • Markov Process
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