Skip to main content

On Walsh's Brownian motions

  • Conference paper
  • First Online:
Séminaire de Probabilités XXIII

Part of the book series: Lecture Notes in Mathematics ((SEMPROBAB,volume 1372))

Research supported in part by National Science Foundation Grant DMS88-01808

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. Barlow, M.T., Pitman, J.W. and Yor, M. (1989). Une extension multidimensionelle de la loi de l'arc sinus. In this volume.

    Google Scholar 

  2. Barlow, M.T., Pitman, J.W. and Yor, M. (1989). Some extensions of the arcsine law. Tech. Report # 189, Dept. Statistics, U.C. Berkeley.

    Google Scholar 

  3. Baxter, J.R. and Chacon, R.V. (1984). The equivalence of diffusions on networks to Brownian motion. Contemp. Math. 26, 33–47.

    Article  MathSciNet  MATH  Google Scholar 

  4. Burdzy, K., Pitman, J.W. and Yor, M. (1989). Some asymptotic laws for crossings and excursions. Colloque Paul Lévy sur les Processus Stochastiques, Astérisque 157–158, 59–74.

    MathSciNet  MATH  Google Scholar 

  5. Davis, M.H.A. and Varaiya, P. (1974). The multiplicity of an increasing family of σ-fields. Ann. Prob. 2, 958–963.

    Article  MathSciNet  MATH  Google Scholar 

  6. El Karoui, N. A propos de la formule d'Azéma-Yor. Sém. Prob. XIII. Lecture Notes in Math. 721, Springer, 443–452.

    Google Scholar 

  7. Frank, H.F. and Durham, S. (1984). Random motion on binary trees. J. Appl. Prob. 21 58–69.

    Article  MathSciNet  MATH  Google Scholar 

  8. Harrison, J.M. and Shepp, L.A. (1981). On skew Brownian motion. Ann. Prob. 9, 309–313.

    Article  MathSciNet  MATH  Google Scholar 

  9. Itô, K. (1970): Poisson point processes attached to Markov processes. Proc. Sixth Berkeley Symp. Math. Statist. Prob. University of California Press, Berkeley, pp. 225–239.

    Google Scholar 

  10. Jacod, J. (1976). A general theorem of representation for martingales. Z. Wahrscheinlichkeitstheorie verw. Gebeite 34, 225–244.

    Article  MathSciNet  MATH  Google Scholar 

  11. Jeulin, T. (1980). Semi-Martingales et Grossissement d'une Filtration. Lecture Notes in Math. 833, Springer-Verlag.

    Google Scholar 

  12. LeGall, J-F (1983). Applications du temps local aux équations différentielles stochastiques unidimensionelles. Sém. Prob. XVII. Lecture Notes in Math. 986, Springer-Verlag, 15–31.

    Article  MathSciNet  Google Scholar 

  13. Le Gall J.F. and Yor M. (1986). Etude asymptotique de certains mouvements browniens avec drift. Probability and Related Fields, 71, 183–229

    Article  MathSciNet  MATH  Google Scholar 

  14. Lindvall, T. and Rogers, L.C.G. (1986). Coupling of multidimensional diffusions by reflection. Ann. Prob. 14, 860–872.

    Article  MathSciNet  MATH  Google Scholar 

  15. Meyer, P.A., Stricker, C. and Yor, M. (1979). Sur une formule de la théorie du balayage. Sém. Prob. XIII. Lecture Notes in Math. 721, Springer-Verlag, 478–487.

    Article  MathSciNet  MATH  Google Scholar 

  16. Millar, P.W. (1977). Germ sigma fields and the natural state space of a Markov process. Z. Wahrscheinlichkeitstheorie verw. Gebeite 39, 85–101.

    Article  MathSciNet  MATH  Google Scholar 

  17. Nakao, S. (1972). On the pathwise uniqueness of solutions of stochastic differential equations. Osaka J. Math. 9, 513–518.

    MathSciNet  MATH  Google Scholar 

  18. Pitman, J. and Yor, M. (1986a). Asymptotic laws of planar Brownian motion. Ann. Prob. 14, 733–779.

    Article  MathSciNet  MATH  Google Scholar 

  19. Rogers, L.C.G. (1983). Itô excursion theory via resolvents. Z. Wahrscheinlichkeitstheorie verw. Gebeite 63, 237–255.

    Article  MATH  Google Scholar 

  20. Salisbury, T.S. (1986). Construction of right processes from excursions. Z. Wahrscheinlichkeitstheorie verw. Gebeite 73, 351–367.

    MathSciNet  MATH  Google Scholar 

  21. Skorokhod, A. V. (1987). Random processes in infinite dimensional spaces (in Russian). Proceedings of the International Congress of Mathematicians: August 3–11, 1986, Berkeley [edited by Andrew M. Gleason]. American Mathematical Society, Providence, R.I., 163–171.

    Google Scholar 

  22. Stricker, C. (1981). Sur un théorème de H. J. Engelbert et J. Hess. Stochastics 6, 73–77.

    Article  MathSciNet  MATH  Google Scholar 

  23. Stroock, D.W. and Yor, M. (1980). On extremal solutions of martingale problems. Ann. Scient. E.N.S., 4ième série, 13, 95–164.

    MathSciNet  MATH  Google Scholar 

  24. Varopoulos, N. Th. (1985). Long range estimates for Markov Chains. Bull. Sci. Math. 109, 225–252.

    MathSciNet  MATH  Google Scholar 

  25. Van der Weide, J.A.M. (1987). Stochastic processes and point processes of excursions. Ph.D. Thesis, Technische Universiteit Delft.

    Google Scholar 

  26. Walsh, J. (1978). A diffusion with a discontinuous local time. In: Temps Locaux, Astérisque 52–53, 37–45.

    Google Scholar 

  27. Weizsäcker, H.v. (1983). Exchanging the order of taking suprema and countable intersection of sigma algebras. Ann. Inst. H. Poincaré 19, 91–100.

    MATH  Google Scholar 

  28. Yor, M. (1978). Sous-espaces denses dans L 1 ou H 1 et représentation des martingales, Sém. Prob. XII, Lecture Notes in Math. 649, Springer, 265–309.

    Article  MATH  Google Scholar 

  29. Yor, M. (1979). Sur le balayage des semi-martingales continues. Sém. Prob. XIII. Lecture Notes in Math. 721, Springer-Verlag, 453–171.

    Article  MathSciNet  MATH  Google Scholar 

  30. Yor, M. (1979). Sur les martingales continues extrémales. Stochastics 2, 191–196.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Jacques Azéma Marc Yor Paul André Meyer

Rights and permissions

Reprints and permissions

Copyright information

© 1989 Springer-Verlag

About this paper

Cite this paper

Barlow, M., Pitman, J., Yor, M. (1989). On Walsh's Brownian motions. In: Azéma, J., Yor, M., Meyer, P.A. (eds) Séminaire de Probabilités XXIII. Lecture Notes in Mathematics, vol 1372. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0083979

Download citation

  • DOI: https://doi.org/10.1007/BFb0083979

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-51191-5

  • Online ISBN: 978-3-540-46176-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics