Skip to main content

The local structure of a class of diffusions and related problems

Part of the Lecture Notes in Mathematics book series (LNM,volume 330)

Keywords

  • Brownian Motion
  • Diffusion Process
  • Poisson Point Process
  • Sample Function
  • Dirichlet Space

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.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   44.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   59.00
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. A. Beurling and J. Deny: Dirichlet spaces, Proc. Nat. Acad. Sci. U.S.A. 45 (1959), 208–215.

    CrossRef  MathSciNet  MATH  Google Scholar 

  2. R.M. Blumenthal and R.K. Getoor: Markov processes and potential theory, Academic Press, New York and London, 1968.

    MATH  Google Scholar 

  3. J. Bretagnolle: Resultats de Kesten sur les processus a accroissements independants, Séminaire de Probabilités V, Lecture note of Math. Vol. 191, Springer, (1971), 21–36.

    MathSciNet  Google Scholar 

  4. Ph. Courrège and P. Priouret: Recollements de processus de Markov, Publ. Inst. Statist. Univ. Paris 14 (1965), 275–377.

    MathSciNet  MATH  Google Scholar 

  5. E.B. Dynkin: Martin boundary for nonnegative solutions of a boundary value problem with a directional derivative, Russian Math. Surveys 19(5), (1964), 1–48.

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. M. Fukushima: On boundary conditions for multi-dimensional Brownian motions with symmetric resolvent densities, Jour. Math. Soc. Japan 21 (1969), 58–93.

    CrossRef  MathSciNet  MATH  Google Scholar 

  7. M. Fukushima: Regular representations of Dirichlet spaces, Trans. Amer. Math. Soc. 155 (1971), 455–473.

    CrossRef  MathSciNet  MATH  Google Scholar 

  8. M. Fukushima: Dirichlet spaces and strong Markov processes, Trans. Amer. Math. Soc. 162 (1971), 185–224.

    CrossRef  MathSciNet  MATH  Google Scholar 

  9. A.R. Galmarino: Representation of an isotropic diffusion as a skew product, Z. Wahrscheinlichkeitstheorie 1 (1963), 359–378.

    CrossRef  MathSciNet  MATH  Google Scholar 

  10. N. Ikeda and S. Watanabe: The local structure of diffusion processes, Seminar on Probability Vol. 35 (1971) (Japanese).

    Google Scholar 

  11. K. Itô: Poisson point processes attached to Markov processes, to appear in Proc. 6-th Berkeley Symp.

    Google Scholar 

  12. K. Itô and H.P. McKean Jr.: Diffusion processes and their sample paths, Springer, Berlin, 1965.

    CrossRef  MATH  Google Scholar 

  13. M. Kanda: Regular points and Green functions in Markov processes, Jour. Math. Soc. Japan 19 (1967), 46–69.

    CrossRef  MathSciNet  MATH  Google Scholar 

  14. H. Kesten: Hitting probabilities of single points for processes with stationary independent increments, Memoir 93. Amer. Math. Soc., (1969).

    Google Scholar 

  15. F. Knight: An infinitesimal decomposition for a class of Markov processes, Ann. Math. Stat. (1970) 5, 1510–1529.

    CrossRef  MathSciNet  MATH  Google Scholar 

  16. H. Kunita and S. Watanabe: On square integrable martingales, Nagoya Math. J. 30 (1967), 209–245.

    MathSciNet  MATH  Google Scholar 

  17. P. Lévy: Processus stochastiques et mouvement brownien, Paris, Gauthier-Villars, 1948.

    MATH  Google Scholar 

  18. H.P. McKean Jr.: Stochastic integrals, Academic Press, 1969.

    Google Scholar 

  19. S.A. Molchanov and E. Ostrovskii: Symmetric stable processes as traces of degenerate diffusion processes, Theory of Prob. and its Appl. 14 (1969), 128–131.

    CrossRef  MathSciNet  MATH  Google Scholar 

  20. M. Motoo: The boundary condition with the discontinuous inclined derivative, Proc. U.S.S.R-Japan Symp. on Probability, Acad. Sci. USSR, Novosibirsk (1969), 247–256.

    Google Scholar 

  21. L. Schwartz: Théorie des distributions, Paris Hermann, 1950–51.

    Google Scholar 

  22. A.V. Skorohod: On the local structure of continuous Markov processes, Theory of Prob. and its Appl. 11 (1966), 336–372.

    CrossRef  MathSciNet  Google Scholar 

  23. T. Takada: Hitting probabilities of single points and local times for Lévy processes. Master Thesis, Kyoto Univ. (1972) (Japanese).

    Google Scholar 

  24. M. Weil: Quasi-processus, Séminaire de Probabilités IV, Lecture notes in Math. 124 (1970), 216–239.

    CrossRef  MathSciNet  MATH  Google Scholar 

  25. A.D. Wentzell: On lateral conditions for multi-dimensional diffusion processes, Theory of Prob. and its Appl. 4 (1959), 164–177.

    CrossRef  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1973 Springer-Verlag

About this paper

Cite this paper

Ikeda, N., Watanabe, S. (1973). The local structure of a class of diffusions and related problems. In: Maruyama, G., Prokhorov, Y.V. (eds) Proceedings of the Second Japan-USSR Symposium on Probability Theory. Lecture Notes in Mathematics, vol 330. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0061485

Download citation

  • DOI: https://doi.org/10.1007/BFb0061485

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-06358-2

  • Online ISBN: 978-3-540-46956-8

  • eBook Packages: Springer Book Archive