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
Sur les points autour desquels le mouvement brownien plan tourne beaucoup
Download PDF
Download PDF
  • Published: March 1994

Sur les points autour desquels le mouvement brownien plan tourne beaucoup

  • Wendelin Werner1 

Probability Theory and Related Fields volume 99, pages 111–144 (1994)Cite this article

We’re sorry, something doesn't seem to be working properly.

Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

Résumé

Nous étudions le comportement asymptotique de l'aireA n de l'ensemble des points autour desquels le mouvement brownien plan a tourné environn fois sur un intervalle de temps fixé [0,t]. Nous montrons en particulier que lorsquen tend vers l'infini,A n est équivalent dansL 2 àt/(2πn 2) asn

Summary

We study the asymptotic behaviour of the areaA n of the set of points around which the planar Brownian motion winds about n times on a given timeinterval [0,t]. We prove thatA n is equivalent (in theL 2-sense) tot/(2πn 2) asn tends to infinity.

Download to read the full article text

Working on a manuscript?

Avoid the common mistakes

Références

  • [CDO] Comtet, A., Desbois, J., Ouvry, S.: Windings of planar Brownian curves. J. Phys. A, Math. Gen.23, 3563–72 (1990)

    Google Scholar 

  • [E] Edwards, S.F.: Statistical mechanics with topological constraints: I. Proc. Phys. Soc.91, 513–519 (1967)

    Google Scholar 

  • [LG] Le Gall, J.F.: Some properties of planar Brownian motion. Cours de l'école d'été de St-Flour 1990 (Lect. Notes Math., Vol. 1527) Berlin Heidelberg New York: Springer, 1992

    Google Scholar 

  • [PY1] Pitman, J., Yor, M.: Asymptotic laws of planar Brownian motion. Ann. Probab.14, 733–779 (1986)

    Google Scholar 

  • [PY2] Pitman, J., Yor, M.: Further asymptotic laws of planar Brownian motion. Ann. Probab.17, 965–1011 (1989)

    Google Scholar 

  • [PS] Port, S.C., Stone, C.J.: Brownian motion and classical potential theory. New York: Academic Press, 1978

    Google Scholar 

  • [RY] Revuz, D., Yor, M.: continuous martingales and Brownian motion. Berlin Heidelberg New York: Springer, 1991

    Google Scholar 

  • [S1] Spitzer, F.: Some theorems concerning two-dimensional Brownian motion. Trans. Am. Math. Soc.87, 187–197 (1958)

    Google Scholar 

  • [S2] Spitzer, F.: Electrostatic capacity, heat flow and Brownian motion. Z. Wahrscheinlichkeitstheor. Verw. Geb.3, 110–121 (1964)

    Google Scholar 

  • [Y] Yor, M.: Loi de l'indice du lacet brownien, et distribution de Hartman-Watson. Z. Wahrscheinlichkeitstheor. Verw. Geb.53, 71–95 (1980)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. C.N.R.S., Laboratoire de Probabilités, Université Pierre et Marie Curie, 4 place Jussieu, F-75252, Paris Cedex 05, France

    Wendelin Werner

Authors
  1. Wendelin Werner
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Werner, W. Sur les points autour desquels le mouvement brownien plan tourne beaucoup. Probab. Th. Rel. Fields 99, 111–144 (1994). https://doi.org/10.1007/BF01199592

Download citation

  • Received: 06 July 1993

  • Revised: 07 December 1993

  • Issue Date: March 1994

  • DOI: https://doi.org/10.1007/BF01199592

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

Mathematics Subject Classification (1991)

  • 60J65
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