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Israel Journal of Mathematics

, Volume 52, Issue 4, pp 361–364 | Cite as

Plane Brownian motion has strictlyn-multiple points

  • Omer Adelman
  • Aryeh Dvoretzky
Article

Abstract

It is shown that, almost surely, for all naturaln, there are points which the plane Brownian motion visitsexactly n times.

Keywords

Brownian Motion Compact Subset Closed Subset Inverse Image Simple Point 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    O. Adelman,Plane Brownian motion, multiple points and order types, to appear.Google Scholar
  2. 2.
    A. Dvoretzky, P. Erdös and S. Kakutani,Multiple points of paths of Brownian motion in the plane, Bull. Res. Counc. Israel, Section F,3 (1954), 364–371.Google Scholar
  3. 3.
    J. F. Le Gal,Sur la measure de Hausdorff des points multiples du mouvement brownien plan, to appear.Google Scholar
  4. 4.
    S. J. Taylor,Sample path properties of processes with stationary independent increments, inStochastic Analysis (D. Kendall and E. Harding, eds.), Wiley and Sons, London, 1973.Google Scholar

Copyright information

© The Weizmann Science Press of Israel 1985

Authors and Affiliations

  • Omer Adelman
    • 1
  • Aryeh Dvoretzky
    • 2
  1. 1.Laboratoire de ProbabilitésUniversité P. & M. CurieParis, Cedex 05France
  2. 2.The Institute for Advanced StudiesThe Hebrew University of JerusalemJerusalemIsrael

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