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Israel Journal of Mathematics

, Volume 4, Issue 2, pp 139–143 | Cite as

Convex hull of Brownian motion ind-dimensions

  • J. R. Kinney
Article

Abstract

We supposeK(w) to be the boundary of the closed convex hull of a sample path ofZ t(w), 0 ≦t ≦ 1 of Brownian motion ind-dimensions. A combinatorial result of Baxter and Borndorff Neilson on the convex hull of a random walk, and a limiting process utilizing results of P. Levy on the continuity properties ofZ t(w) are used to show that the curvature ofK(w) is concentrated on a metrically small set.

Keywords

Brownian Motion Random Walk Convex Hull Meromorphic Function Sample Path 
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. Barndorff-Nielson and G. Baxter,Combinational lemmas in n-dimensions, Trans. Amer. Math. Soc.108 (1963), 313–325.CrossRefMathSciNetGoogle Scholar
  2. 2.
    L. Carleson,On a class of meromorphic functions and its associated exceptional sets. Thesis, University of Uppsala, (1950).Google Scholar
  3. 3.
    J. R. Kinney,The convex hull of plane Brownian motion, Ann. Math. Statist.34 (1963), 327–329.MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    P. Lévy,Processus stochastiques et mouvement Brownien, Gautier-Villars, Paris, 1948.MATHGoogle Scholar

Copyright information

© Hebrew University 1966

Authors and Affiliations

  • J. R. Kinney
    • 1
  1. 1.Michigan State UniversityEast Lansing

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