Advertisement

Components of the Strong Markov Property

  • Olav Kallenberg
Part of the Trends in Mathematics book series (TM)

Summary

The strong Markov property of a process X at an optional time π < ∞ may be thought of as a combination of the conditional independence XT+hM-xrFT with the homogeneity for a suitable set of probability kernels. In an earlier paper, a stronger version of the latter condition was shown to imply the former property. Our present aim is to examine to what extent the two properties are in fact equivalent

Keywords

Homogeneity Condition Conditional Independence Markov Property Optional Time Conditional Inde 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Blumenthal, R.M., Getoor, R.K. Markov Processes and Potential Theory. Academic Press, New York (1968).zbMATHGoogle Scholar
  2. Dellacherie, C, Meyer, P.A. Probabilités et Potentiel, Chap. I-IV. Hermann, Paris (1975).zbMATHGoogle Scholar
  3. Kallenberg, O. Characterizations and embedding properties in exchangeability. Z. Wahrscheinlichkeitstheorie verw. Gebiete 60, 249–281 (1982).MathSciNetzbMATHCrossRefGoogle Scholar
  4. Kallenberg, O. Homogeneity and the strong Markov property. Ann. Probab. 15, 213–240 (1987).MathSciNetzbMATHCrossRefGoogle Scholar
  5. Kallenberg, O. Foundations of Modern Probability. Springer, New York (1997).zbMATHGoogle Scholar
  6. Walsh, J.B. Transition functions of Markov processes. In: Séminaire de Probabilités VI, Lecture Notes in Mathematics 258, 215–232. Springer, Berlin (1972).Google Scholar

Copyright information

© Springer Science+Business Media New York 1998

Authors and Affiliations

  • Olav Kallenberg
    • 1
  1. 1.Department of MathematicsAuburn UniversityAuburnUSA

Personalised recommendations