Skip to main content

Part of the book series: Grundlehren der mathematischen Wissenschaften ((GL,volume 293))

  • 1357 Accesses

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 74.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Notes and Comments

  1. Pazy, A.Semi-groups of linear operators and applications to partial differential equations. (Applied Mathematical Sciences, vol. 44 ). Springer, Berlin Heidelberg New York 1983

    Google Scholar 

  2. 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 - 113

    Google Scholar 

  3. Kunita, H. Absolute continuity of Markov processes and generators. Nagoya Math. J. 36 (1969) 1 - 26

    Google Scholar 

  4. Roth, J.P. Opérateurs dissipatifs et semi-groupes dans les espaces de fonctions continues. Ann. Inst. Fourier 26 (1976) 1 - 97

    Google Scholar 

  5. Chen, L.H.Y. Poincaré-type inequalities via stochastic integrals. Z.W. 69 (1985) 251 - 277

    Article  MATH  Google Scholar 

  6. 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 - 141

    Google Scholar 

  7. Stroock, D.W., and Varadhan, S.R.S. Multidimensional diffusion processes. Springer, Berlin Heidelberg New York 1979

    MATH  Google Scholar 

  8. 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 - 113

    Google Scholar 

  9. Dynkin, E.B. arkov processes. Springer, Berlin Heidelberg New York 1965

    Google Scholar 

  10. Itô, K., and McKean, H.P.Diffusion processes and their sample paths. Springer, Berlin Heidelberg New York 1965

    Book  Google Scholar 

  11. Freedman, D. rownian motion and diffusion. Holden-Day, San Fransisco 1971

    Google Scholar 

  12. Mandl, P. Analytical treatment of one-dimensional Markov process. Springer, Berlin Heidelberg New York 1968

    Google Scholar 

  13. Breiman, L. Probability. Addison-Wesley Publ. Co, Reading, Mass. 1968

    Google Scholar 

  14. Nagasawa, M. Time reversions of Markov processes. Nagoya Math. J. 24 (1964) 177 - 204

    MathSciNet  Google Scholar 

  15. Meyer, P.A. Processus de Markov: La frontière de Martin. Lecture Notes in Mathematics, vol. 77. Springer, Berlin Heidelberg New York 1970

    Google Scholar 

  16. Meyer, P.A. Processus de Markov. Lecture Notes in Mathematics, vol. 26, Springer, Berlin Heidelberg New York 1967

    Google Scholar 

  17. Williams, D. Path decomposition and continuity of local time for one dimensional diffusions I. Proc. London Math. Soc. (3) 28 (1974) 738 - 768

    Article  MATH  Google Scholar 

  18. Williams, D. Decomposing the Brownian path. Bull. Amer. Math. Math. Soc. 76 (1970) 871 - 873

    Google Scholar 

  19. Yor, M. A propos de l’inverse du mouvement brownien dans B" (n z 3). Ann. I.H.P. 21, 1 (1985) 27 - 38

    MathSciNet  MATH  Google Scholar 

  20. 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 1981

    Google Scholar 

  21. Getoor, R.K. he Brownian escape process. Ann. Prob. 7 (1979) 864 - 867

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 1991 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Revuz, D., Yor, M. (1991). Generators and Time Reversal. In: Continuous Martingales and Brownian Motion. Grundlehren der mathematischen Wissenschaften, vol 293. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-21726-9_8

Download citation

  • DOI: https://doi.org/10.1007/978-3-662-21726-9_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-21728-3

  • Online ISBN: 978-3-662-21726-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics