Skip to main content

Branching processes, the Ray-Knight theorem, and sticky Brownian motion

  • Conference paper
  • First Online:
Séminaire de Probabilités XXXI

Part of the book series: Lecture Notes in Mathematics ((SEMPROBAB,volume 1655))

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 49.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 65.00
Price excludes VAT (USA)
  • 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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. M. Amir. Sticky Brownian motion as the strong limit of a sequence of random walks. Stochastic Processes and their Applications, 39:221–237, 1991.

    Article  MathSciNet  MATH  Google Scholar 

  2. R.J. Chitashvili. On the nonexistence of a strong solution in the boundary problem for a sticky Brownian motion. Technical Report BS-R8901, Centre for Mathematics and Computer Science, Amsterdam, 1989.

    MATH  Google Scholar 

  3. W. Feller. On boundaries and lateral conditions for the Kolmogorov equations. Annals of Mathematics, Series 2, 65:527–570, 1957.

    Article  MathSciNet  MATH  Google Scholar 

  4. J.M. Harrison and A.J. Lemoine. Sticky Brownian motion as the limit of storage processes. Journal of Applied Probability, 18:216–226, 1981.

    Article  MathSciNet  MATH  Google Scholar 

  5. N. Ikeda and S. Watanabe. Stochastic Differential Equations and Diffusion Processes. North Holand-Kodansha, Amsterdam and Tokyo, 1981.

    MATH  Google Scholar 

  6. F.B. Knight. Essentials of Brownian motion and Diffusion, volume 18 of Mathematical Surveys. American Mathematical Society, Providence, Rhode-Island, 1981.

    Book  Google Scholar 

  7. J.F. Le Gall. Cours de troisième cycle. Laboratoire de Probabilités, Paris 6. 1994.

    Google Scholar 

  8. J.W. Pitman and M. Yor. A decomposition of Bessel bridges. Zeitschrift für Wahrscheinlichkeitstheorie, 59:425–457, 1982.

    Article  MathSciNet  MATH  Google Scholar 

  9. D. Revuz and M. Yor. Continuous martingales and Brownian motion. Springer, Berlin, 1991.

    Book  MATH  Google Scholar 

  10. L.C.G. Rogers and D. Williams. Diffusions, Markov processes and Martingales, vol 2: Itô calculus. Wiley, New York, 1987.

    MATH  Google Scholar 

  11. T. Shiga and S. Watanabe. Bessel diffusions as a one-parameter family of diffusion processes. Zeitschrift für Wahrscheinlichkeitstheorie, 27:37–46, 1973.

    Article  MathSciNet  MATH  Google Scholar 

  12. K. Yamada. Reflecting or sticky Markov processes with Lévy generators as the limit of storage processes. Stochastic Processes and their Applications, 52:135–164, 1994.

    Article  MathSciNet  MATH  Google Scholar 

  13. M. Yor. Some remarks concerning sticky Brownian motion. Unpublished, 1989.

    Google Scholar 

  14. M. Yor. Some aspects of Brownian motion, part 1: Some special functionals. Birkhäuser, 1992.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Jacques Azéma Marc Yor Michel Emery

Rights and permissions

Reprints and permissions

Copyright information

© 1997 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Warren, J. (1997). Branching processes, the Ray-Knight theorem, and sticky Brownian motion. In: Azéma, J., Yor, M., Emery, M. (eds) Séminaire de Probabilités XXXI. Lecture Notes in Mathematics, vol 1655. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0119287

Download citation

  • DOI: https://doi.org/10.1007/BFb0119287

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-62634-3

  • Online ISBN: 978-3-540-68352-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics