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Séminaire de Probabilités XIX 1983/84 pp 63–79Cite as

On local times of a diffusion

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Part of the book series: Lecture Notes in Mathematics ((SEMPROBAB,volume 1123))

Abstract

In this note we consider local time of a regular, transient diffusion as a density of a occupation measure, on the one hand, and as a dual predictable projection, on the other hand. The essential tool in our discussion is the Doob-Meyer decomposition for submartingales.

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References

  1. Azema, J. et Yor, M.: En quise d'introduction. Société Mathématique de France, Astérisque 52–53 (1978), 3–16.

    Google Scholar 

  2. Blumenthal, R.M. and Getoor, R.K.: Markov Processes and Potential Theory. Academic Press, New York (1968).

    MATH  Google Scholar 

  3. Cinlar, E., Jacod, J., Protter, P. and Sharpe, M.J.: Semimartingales and Markov processes. Z. Wahrscheinlichkeitstheorie verw. Gebiete 54 (1980), 161–219.

    Article  MathSciNet  MATH  Google Scholar 

  4. Dellacherie, C.: Capacités et processus stochastiques. Springer Verlag, Berlin-Heidelberg-New York (1972).

    MATH  Google Scholar 

  5. Ikeda, N. and Watanabe, S.: Stochastic differential equations and Diffusion Processes. North-Holland/Kodansha, Amsterdam-Oxford-New York/Tokyo (1981).

    MATH  Google Scholar 

  6. Itô, K. and McKean, H.: Diffusion Processes and their sample paths. Springer Verlag, Berlin-Heidelberg-New York (1974).

    MATH  Google Scholar 

  7. Jacod, J.: Calcul Stochastique et Problèmes de Martingales, Lecture notes in Mathematics 714. Springer-Verlag, Berlin-Heidelberg-New York (1979).

    Book  MATH  Google Scholar 

  8. Jeulin, T.: Application de la Theorie du Grossissement a l'etude des temps locaux Browniens. Université Pierre et Marie Curie, Laboratoire de Probabilités (Report).

    Google Scholar 

  9. Meyer, P.A.: Un cours sur les intégrales stochastiques, Séminaire de Probabilités X, Lecture notes in Mathematics 511, Springer Verlag, Berlin-Heidelberg-New York (1976), 246–400.

    Google Scholar 

  10. Pitman, J. and Yor, M.: Bessel processes and infinitely divisible laws; Stochastic integrals, Proc. LMS Durham Symp. 1981, Lecture notes in Mathematics 851. Springer-Verlag, Berlin-Heidelberg-New York (1981), 285–370.

    Google Scholar 

  11. Rao, M.: On decomposition theorems of Meyer. Mathematica Scandinavica 24 (1969), 66–78.

    MathSciNet  MATH  Google Scholar 

  12. Salminen, P.: One-dimensional diffusions and their exit spaces. To appear in Mathematica Scandinavica.

    Google Scholar 

  13. Salminen, P.: Optimal stopping of one-dimensional diffusions. Submitted for publication.

    Google Scholar 

  14. Walsh, J.B.: A diffusion with a discontinuous local time. Société Mathématique de France, Astérisque 52–53 (1978), 37–46.

    Google Scholar 

  15. Williams, D.: Diffusions, Markov processes, and Martingales. John Wiley and Sons, Chichester-New York-Brisbane-Toronto (1979).

    Google Scholar 

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Authors and Affiliations

  1. Mathematical Institute, Åbo Akademi, SF-20500, Åbo 50, Finland

    P. Salminen

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  1. P. Salminen
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Jacques Azéma Marc Yor

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© 1985 Springer-Verlag

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Salminen, P. (1985). On local times of a diffusion. In: Azéma, J., Yor, M. (eds) Séminaire de Probabilités XIX 1983/84. Lecture Notes in Mathematics, vol 1123. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0075839

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  • DOI: https://doi.org/10.1007/BFb0075839

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-15230-9

  • Online ISBN: 978-3-540-39397-9

  • eBook Packages: Springer Book Archive

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