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Generators and Time Reversal

  • Daniel Revuz
  • Marc Yor
Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 293)

Abstract

In this chapter, we take up the study of Markov processes. We assume that the reader has read Sect. 1 and 2 in Chap. III.

Keywords

Markov Process Time Reversal Markov Property Speed Measure Borel Function 
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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Notes and Comments

  1. 1.
    Pazy, A.Semi-groups of linear operators and applications to partial differential equations. (Applied Mathematical Sciences, vol. 44 ). Springer, Berlin Heidelberg New York 1983Google Scholar
  2. 1.
    Dellacherie, C. Meyer, P.A. and Yor, M. Sur certaines propriétés des espaces H’ et BMO. Sém. Prob. XII. Lecture Notes in Mathematics, vol. 649. Springer, Berlin Heidelberg New York 1978, pp. 98 - 113Google Scholar
  3. 1.
    Kunita, H. Absolute continuity of Markov processes and generators. Nagoya Math. J. 36 (1969) 1 - 26Google Scholar
  4. 1.
    Roth, J.P. Opérateurs dissipatifs et semi-groupes dans les espaces de fonctions continues. Ann. Inst. Fourier 26 (1976) 1 - 97Google Scholar
  5. 1.
    Chen, L.H.Y. Poincaré-type inequalities via stochastic integrals. Z.W. 69 (1985) 251 - 277zbMATHCrossRefGoogle Scholar
  6. 5.
    Kunita, H. Some extensions of Itô’s formula. Sém. Prob. XV. Lecture Notes in Mathematics, vol. 850. Springer, Berlin Heidelberg New York 1981, pp. 118 - 141Google Scholar
  7. 1.
    Stroock, D.W., and Varadhan, S.R.S. Multidimensional diffusion processes. Springer, Berlin Heidelberg New York 1979zbMATHGoogle Scholar
  8. 1.
    Priouret, P. Processus de diffusion et équations différentielles stochastiques. Ecole d’Eté de Probabilités de Saint-Flour III. Lecture Notes in Mathematics, vol. 390. Springer, Berlin Heidelberg New York 1974, pp. 38 - 113Google Scholar
  9. 1.
    Dynkin, E.B. arkov processes. Springer, Berlin Heidelberg New York 1965Google Scholar
  10. 1.
    Itô, K., and McKean, H.P.Diffusion processes and their sample paths. Springer, Berlin Heidelberg New York 1965CrossRefGoogle Scholar
  11. 1.
    Freedman, D. rownian motion and diffusion. Holden-Day, San Fransisco 1971Google Scholar
  12. 1.
    Mandl, P. Analytical treatment of one-dimensional Markov process. Springer, Berlin Heidelberg New York 1968Google Scholar
  13. 1.
    Breiman, L. Probability. Addison-Wesley Publ. Co, Reading, Mass. 1968Google Scholar
  14. 1.
    Nagasawa, M. Time reversions of Markov processes. Nagoya Math. J. 24 (1964) 177 - 204MathSciNetGoogle Scholar
  15. 2.
    Meyer, P.A. Processus de Markov: La frontière de Martin. Lecture Notes in Mathematics, vol. 77. Springer, Berlin Heidelberg New York 1970Google Scholar
  16. 1.
    Meyer, P.A. Processus de Markov. Lecture Notes in Mathematics, vol. 26, Springer, Berlin Heidelberg New York 1967Google Scholar
  17. 3.
    Williams, D. Path decomposition and continuity of local time for one dimensional diffusions I. Proc. London Math. Soc. (3) 28 (1974) 738 - 768zbMATHCrossRefGoogle Scholar
  18. 2.
    Williams, D. Decomposing the Brownian path. Bull. Amer. Math. Math. Soc. 76 (1970) 871 - 873Google Scholar
  19. 16.
    Yor, M. A propos de l’inverse du mouvement brownien dans B" (n z 3). Ann. I.H.P. 21, 1 (1985) 27 - 38MathSciNetzbMATHGoogle Scholar
  20. 1.
    Pitman, J.W., and Yor, M. Bessel processes and infinitely divisible laws. In: D. Williams (ed.) Stochastic integrals. Lecture Notes in Mathematics, vol. 851. Springer, Berlin Heidelberg New York 1981Google Scholar
  21. 2.
    Getoor, R.K. he Brownian escape process. Ann. Prob. 7 (1979) 864 - 867MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Daniel Revuz
    • 1
  • Marc Yor
    • 2
  1. 1.Département de MathématiquesUniversité de Paris VIIParis Cedex 05France
  2. 2.Laboratoire de ProbabilitésUniversité Pierre et Marie CurieParis Cedex 05France

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