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Localizations of Feller infinitesimal generators and uniqueness of corresponding killed processes

Part of the Lecture Notes in Mathematics book series (LNM,volume 1379)

Abstract

Let G be infinitesimal generator of a Feller transition semigroup on a compact C manifold M with boundary. Assume that G is defined by means of a sufficiently smooth integrodifferential elliptic boundary system of Ventcel. Let U be an open subset of M/∂M. Then the operator uniquely determines the canonical cadlag Markov process corresponding to G before its first exit time from U. This statement is formulated and proved in rigorous measure theoretical language.

Keywords

  • Probability Measure
  • Open Subset
  • Elliptic System
  • Exit Time
  • Infinitesimal Generator

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References

  1. P. Billingsley, Convergence of Probability Measures, John Wiley and Sons, Inc., 1968.

    Google Scholar 

  2. R.M. Blumenthal and R.K. Getoor, Markov Processes and Potential Theory, Academic Press, 1968.

    Google Scholar 

  3. J.-M. Bony, Ph. Courrége et P. Priouret, Semi-groupes de Feller sur une variété a bord compacte et problémes aux limites intégro-différentielles du second ordre donnant lieu au principe du maximum, Ann. Inst. Fourier 18, 2 (1968), p. 369–521.

    CrossRef  MathSciNet  MATH  Google Scholar 

  4. E.B. Dynkin, Markov Processes, Vol. I, Springer-Verlag, 1965.

    Google Scholar 

  5. S.N. Ethiér and T.G. Kurtz, Markov Processes, Characterization and Convergence, John Wiley and Sons, 1986.

    Google Scholar 

  6. I.I. Gichman and A.V. Skorochod, Theory of Stochastic Processes, Vol. I (in russian), "Nauka", Moscow, 1971.

    Google Scholar 

  7. 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.

    MathSciNet  MATH  Google Scholar 

  8. K. Itô and H. Mc Kean, Diffusion processes and their sample paths, Springer-Verlag, 1965.

    Google Scholar 

  9. J. Kisyński, On a formula of N. Ikeda and S. Watanabe concerning the Lévy kernel, p. 260–279 in "Probability Measures on Groups VII", Lecture Notes in Mathematics, Vol. 1064, Springer-Verlag, 1984.

    Google Scholar 

  10. J. Kisyński, On jumps of paths of Markov processes, p.130–145 in "Probability Measures on Groups VIII", Lecture Notes in Mathematics, Vol. 1210, Springer-Verlag, 1986.

    Google Scholar 

  11. K. Sato and T. Ueno, Multi-dimensional diffusion and the Markov process on the boundary, J. Math. Kyoto Univ. 4 (1965), p. 529–605.

    MathSciNet  MATH  Google Scholar 

  12. W. von Waldenfels, Fast positive Operatoren, Zeitschrift für Wahrscheinlichkeitstheorie 4 (1965), p. 159–174.

    CrossRef  MathSciNet  MATH  Google Scholar 

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© 1989 Springer-Verlag

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Kisyński, J. (1989). Localizations of Feller infinitesimal generators and uniqueness of corresponding killed processes. In: Heyer, H. (eds) Probability Measures on Groups IX. Lecture Notes in Mathematics, vol 1379. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0087852

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  • DOI: https://doi.org/10.1007/BFb0087852

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  • Print ISBN: 978-3-540-51401-5

  • Online ISBN: 978-3-540-46206-4

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