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
Etude asymptotique des enlacements du mouvement brownien autour des droites de l'espace
Download PDF
Download PDF
  • Published: April 1987

Etude asymptotique des enlacements du mouvement brownien autour des droites de l'espace

  • J. F. Le Gall1 &
  • M. Yor1 

Probability Theory and Related Fields volume 74, pages 617–635 (1987)Cite this article

  • 74 Accesses

  • Metrics details

Summary

The existence of a joint asymptotic distribution for the windings of a three-dimensional Brownian motion around a finite number of straight lines is obtained. This complements the recent studies, by Pitman- Yor, and the authors, of the joint asymptotic distribution for the windings of planar Brownian motion around a finite number of points.

The following principle governs the passage from results in the plane to results in space:

Let B be a three-dimensional Brownian motion, and P 1, ..., P k, k planes which intersect two by two. Then, the convergences in distribution concerning the planar Brownian motions B i (1≦i≦k), defined respectively as the orthogonal projections of B on P i (1≦i≦k), take place jointly, and the corresponding limit variables are independent.

Download to read the full article text

Working on a manuscript?

Avoid the common mistakes

References

  1. Jeulin, T., Yor, M.: Sur les distributions de certaines fonctionnelles du mouvement brownien. Sém. Probas XV. Lect. Notes Math. 850. Berlin, Heidelberg, New York: Springer 1981

    Google Scholar 

  2. 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 

  3. Knight, F.B.: On sojourn times of killed Brownian motion. Sém. Probas XII. Lect. Notes Math. 649. Berlin, Heidelberg, New York: Springer 1978

    Google Scholar 

  4. Le Gall, J.F., Yor, M.: Etude asymptotique de certains mouvements browniens complexes avec drift. Probab. Th. Rel. Fields 71, 183–229 (1986)

    Google Scholar 

  5. Le Gall, J.F. Yor, M.: Sur certaines lois limites intervenant dans l'étude des enlacements du mouvement brownien dans ℝ3. En préparation

  6. Le Gall, J.F., Yor, M.: Excursions browniennes et carrés de processus de Bessel. Comptes Rendus Acad. Sci. Paris, t. 303 (Série I, 3), 73–76 (1986)

    Google Scholar 

  7. Le Gall, J.F., Yor, M.: Enlacements du mouvement brownien autour des courbes de l'espace. En préparation

  8. Messulam, P., Yor, M.: On D. Williams “pinching method” and some applications. J. Lond. Math. Soc. (2), 26, 348–364 (1982)

    Google Scholar 

  9. Pitman, J.W., Yor, M.: Asymptotic laws of planar Brownian motion. Ann. Probab. (special invited paper) 14, 733–779 (1986)

    Google Scholar 

  10. Spitzer, F.: Some theorems concerning 2-dimensional Brownian motion. Trans. Am. Math. Soc. 87, 187–197 (1958)

    Google Scholar 

  11. Pitman, J.W., Yor, M.: Some divergent integrals of Brownian motion. Adv. Appl. Probab., Supplement to Vol. 18, n° 4, December 1985

Download references

Author information

Authors and Affiliations

  1. Laboratoire de Calcul des Probabilités, 4, Université P. et M. Curie, Place Jussieu, F-75252, Paris Cedex 05, 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

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Le Gall, J.F., Yor, M. Etude asymptotique des enlacements du mouvement brownien autour des droites de l'espace. Probab. Th. Rel. Fields 74, 617–635 (1987). https://doi.org/10.1007/BF00363519

Download citation

  • Received: 30 November 1985

  • Revised: 25 September 1986

  • Issue Date: April 1987

  • DOI: https://doi.org/10.1007/BF00363519

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