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On jumps of paths of Markov processes

  • Jan Kisyński
Research Articles
Part of the Lecture Notes in Mathematics book series (LNM, volume 1210)

Abstract

Let X be a cadlag Markov process with separable metric state space S, governed by semigroup of transition kernels (Nt)t≥0. Let f be a bounded, non-negative, continuous function on S2, vanishing in a uniform neighbourhood of the diagonal. Define Open image in new window and suppose that sup{|Jtf(x)|: t>0, x εS}<∞ and that Open image in new window exists for each xεS. Then Open image in new window du for each t≥0 and each xεS.

Keywords

Markov Process Borel Function Infinitesimal Generator Disjoint Support Transition Semigroup 
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.

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References

  1. [1]
    R.M. Blumenthal and R.K. Getoor, Markov Processes and Potential Theory, Academic Press, 1968.Google Scholar
  2. [2]
    C. Dellacherie and P.-A. Meyer, Probabilities and Potential, North Holland Mathematics Studies 29, 1978.Google Scholar
  3. [3]
    E.B. Dynkin, A.A. Yuschkewitsch, Sätze und Aufgaben über Markoffsche Prozesse, Springer-Verlag, 1969.Google Scholar
  4. [4]
    W. Feller, An Introduction to Probability Theory and its Applications, Wiley and Sons, Inc., 1966.Google Scholar
  5. [5]
    N. Ikeda and S. Watanabe, On some relations between the harmonic measure and the Lévy measure for a certain class of Markov processes, J. Math. Kyoto Univ. 2 (1962), p. 79–95.MathSciNetzbMATHGoogle Scholar
  6. [6]
    J. Kisyński, On a formula of N. Ikeda and S. Watanabe concerning the Levy kernel, p. 260–279 in "Probability Measures on Groups VII", Lecture Notes in Mathematics, Vol. 1064, Springer-Verlag, 1984.Google Scholar
  7. [7]
    J. Iamperti, Stochastic Processes, a Survey of the Mathematical Theory, Applied Mathematical Sciences, Vol. 23, Springer-Verlag, 1977.Google Scholar
  8. [8]
    P.-A. Meyer, Probability and Potentials, Blaisdell Publishing Company, 1966.Google Scholar
  9. [9]
    K.R. Parthasarathy, Introduction to Probability and Measure, 1980 (russian translation, "Mir", 1983).Google Scholar
  10. [10]
    S. Watanabe, On discontinuous additive functionals and Lévy measures of a Markov process, Japanese J. Math. 34, 1964, p. 53–70.zbMATHGoogle Scholar
  11. [11]
    A.D. Ventcel, A course of the Theory of Stochastic Processes (in russian), "Nauka", Moscow, 1975.zbMATHGoogle Scholar

Copyright information

© Springer-Verlag 1986

Authors and Affiliations

  • Jan Kisyński
    • 1
  1. 1.Technical University of LublinLublinPoland

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