Skip to main content

Advertisement

SpringerLink
Log in
Menu
Find a journal Publish with us
Search
Cart
  1. Home
  2. Probability Theory and Related Fields
  3. Article
Étude asymptotique de certains mouvements browniens complexes avec drift
Download PDF
Download PDF
  • Published: January 1986

Étude asymptotique de certains mouvements browniens complexes avec drift

  • J. F. Le Gall1 &
  • M. Yor1 

Probability Theory and Related Fields volume 71, pages 183–229 (1986)Cite this article

  • 109 Accesses

  • 27 Citations

  • Metrics details

Download to read the full article text

Working on a manuscript?

Avoid the common mistakes

References

  1. Azema, J., Duflo, M., Revuz, D.: Mesure invariante des processus de Markov récurrents. Séminaire de Probabilités III. Lect. Notes Math. 88, p. 24–33. Berlin-Heidelberg-New York: Springer 1969

    Google Scholar 

  2. Burkholder, D.: Distribution function inequalities for martingales. Ann. Probab. 1, 19–42 (1973)

    Google Scholar 

  3. Dambis, K.: On the decomposition of continuous submartingales. Teor. Verojatn. Primen. 10, 438–448 (1965)

    Google Scholar 

  4. Dubins, L.E., Schwartz, G.: On continuous martingales. Proc. Natl. Acad. Sci. USA 53, 913–916 (1965)

    Google Scholar 

  5. Durrett, R.: A new proof of Spitzer's result on the winding of two dimensional Brownian motion. Ann. Probab. 10, 244–246 (1982)

    Google Scholar 

  6. Friedman, A., Pinsky, M.A.: Asymptotic behavior of solutions of linear stochastic systems. Trans. Am. Math. Soc. 181, 1–22 (1973)

    Google Scholar 

  7. Friedman, A., Pinsky, M.A.: Asymptotic stability and spiraling properties for solutions of stochastic equations. Trans. Am. Math. Soc. 186, 331–358 (1973)

    Google Scholar 

  8. Harrison, J.M., Shepp, L.A.: On skew brownian motion. Ann. Probab. 9, 309–313 (1981)

    Google Scholar 

  9. Hashminskii, R.Z.: Ergodic properties of recurrent diffusion processes and stabilization of the solution to the Cauchy problem for parabolic equations. Teor. Verojatnost Primen. 5, 196–214 (1960)

    Google Scholar 

  10. Ikeda, N., Watanabe, S.: Stochastic differential equations and diffusion processes. Kodansha: North Holland Mathematical Library, 1981

    Google Scholar 

  11. Itô, K., Mc Kean, H.P.: Diffusion processes and their sample paths. Berlin-Heidelberg-New York: Springer 1965

    Google Scholar 

  12. Kasahara, Y., Kotani, S.: On limit processes for a class of additive functionals of recurrent diffusion processes. Z. Wahrscheinlichkeitstheor. Verw. Geb. 49, 133–153 (1979)

    Google Scholar 

  13. Knight, F.B.: A reduction of continuous square integrable martingales to Brownian motion. Lect. Notes Math. 190. Berlin-Heidelberg-New York: Springer 1971

    Google Scholar 

  14. Le Gal., J.F.: One-dimensional stochastic differential equations involving the local times of the unknown process. In: Stochastic analysis. Lect. Notes Math. 1095, 51–82. Berlin-Heidelberg-New York-Tokyo: Springer 1984

    Google Scholar 

  15. Lyons, T., Mc Kean, H.P.: Windings of the plane Brownian motion. Adv. Math. 51, 212–225 (1984)

    Google Scholar 

  16. Messulam, P., Yor, M.: On D. Williams' “pinching method” and some applications. J. Lond. Math. Soc. 26, 348–364 (1982)

    Google Scholar 

  17. Pitman, J.W., Yor, M.: The asymptotic joint distribution of windings of planar Brownian motion. Bull. Am. Math. Soc. 10, 109–111 (1984)

    Google Scholar 

  18. Pitman, J.W., Yor, M.: Asymptotic laws of planar Brownian motion. A paraître dans Annals of Probability (1985). Preprint University of California, Berkeley (1984)

  19. Rosenkrantz, W.: Limit theorems for solutions to a class of stochastic differential equations. Indiana Univ. Math. J. 24, 613–625 (1975)

    Google Scholar 

  20. Spitzer, F.: Some theorems concerning two-dimensional Brownian motion. Trans. Am. Math. Soc. 87, 187–197 (1958)

    Google Scholar 

  21. Stroock, D.W., Varadhan, S.R.S.: Multidimensional diffusion processes. Berlin-Heidelberg-New York: Springer 1979

    Google Scholar 

  22. Veretennikov, A.Y.: On strong solutions of some stochastic equations. Russ. Math. Surv. 35, 5, 215–216 (1978)

    Google Scholar 

  23. Walsh, J.B.: A diffusion with discontinuous local time. Astérisque 52–53, 37–45 (1978)

    Google Scholar 

  24. Watanabe, S.: A limit theorem for sums of i.i.d. random variables with slowly varying tail probability. In: Multivariate Analysis, p. 249–261. Krishnaiah, P.R. (ed.). Amsterdam: North Holland 1980

    Google Scholar 

  25. Williams, D.: A simple geometric proof of Spitzer's winding number formula for two dimensional Brownian motion. Unpublished manuscript, University College, Swansea (1974)

    Google Scholar 

  26. Yor, M.: Une décomposition asymptotique du nombre de tours du mouvement brownien complexe. Colloque en l'honneur de Laurent Schwartz (mai 1983). A paraître dans Astérisque (1985)

  27. Yor, M.: Sur la continuité des temps locaux associés à certaines semi-martingales. Astérisque 52–53, 23–35 (1978)

    Google Scholar 

  28. Zvonkin, A.K.: A transformation of the phase space of a process that removes the drift. Math. U.S.S.R. Sb 22, 129–149 (1974)

    Google Scholar 

  29. Le Gall, J.F.: Sur la saucisse de Wiener et les points multiples du mouvement brownien. A paraître dans Ann. Probab. (1985)

  30. Jeulin, T.: Application de la théorie du grossissement à l'étude des temps locaux Browniens. Lect. Notes Math. 1118. Berlin-Heidelberg-New York-Tokyo: Springer 1985

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Laboratoire de Calcul des Probabilités, Université P. et M. Curie, 4, Place Jussieu, F-75230, Paris (5e), France

    J. F. Le Gall & M. Yor

Authors
  1. J. F. Le Gall
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Yor
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

La recherche de cet auteur a été réalisée en partie avec l'aide de NSF Grant MCS 82-02552

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Le Gall, J.F., Yor, M. Étude asymptotique de certains mouvements browniens complexes avec drift. Probab. Th. Rel. Fields 71, 183–229 (1986). https://doi.org/10.1007/BF00332310

Download citation

  • Received: 15 July 1984

  • Revised: 25 May 1985

  • Issue Date: January 1986

  • DOI: https://doi.org/10.1007/BF00332310

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

Download PDF

Working on a manuscript?

Avoid the common mistakes

Advertisement

Search

Navigation

  • Find a journal
  • Publish with us

Discover content

  • Journals A-Z
  • Books A-Z

Publish with us

  • Publish your research
  • Open access publishing

Products and services

  • Our products
  • Librarians
  • Societies
  • Partners and advertisers

Our imprints

  • Springer
  • Nature Portfolio
  • BMC
  • Palgrave Macmillan
  • Apress
  • Your US state privacy rights
  • Accessibility statement
  • Terms and conditions
  • Privacy policy
  • Help and support

167.114.118.210

Not affiliated

Springer Nature

© 2023 Springer Nature