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The Exact Hausdorff Measure of Brownian Multiple Points

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Seminar on Stochastic Processes, 1986

Part of the book series: Progress in Probability and Statistics ((PRPR,volume 13))

Abstract

Let B = (Bt,t ≧0) denote a d-dimensional Brownian motion, with d ≧ 2. Dvoretzky, Erdös, Kakutani and Taylor [2,3,4] have proved that the path of B has points of multiplicity p ≧ 2 if and only if one of the two following conditions is satisfied:

$$\frac{-d=2,p arbitrary}{-d=3,p=2} $$
(1.a)

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Authors and Affiliations

  1. Laboratoire de Probabilités, Universite P. et M. Curie, 4, place Jussieu - Tour 56, F - 75252, Paris Cedex 05, France

    Jean-François Le Gall

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  1. Jean-François Le Gall
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Editor information

Editors and Affiliations

  1. Civil Engineering Department, Princeton University, 08544, Princeton, NJ, USA

    E. Çinlar

  2. Department of Mathematics, Stanford University, 94305, Stanford, CA, USA

    K. L. Chung

  3. Department of Mathematics, University of California, 92093, La Jolla, CA, USA

    R. K. Getoor

  4. Department of Mathematics, University of Florida, 32611, Gainesville, FL, USA

    J. Glover

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© 1987 Birkhäuser Boston

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Le Gall, JF. (1987). The Exact Hausdorff Measure of Brownian Multiple Points. In: Çinlar, E., Chung, K.L., Getoor, R.K., Glover, J. (eds) Seminar on Stochastic Processes, 1986. Progress in Probability and Statistics, vol 13. Birkhäuser Boston. https://doi.org/10.1007/978-1-4684-6751-2_8

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  • DOI: https://doi.org/10.1007/978-1-4684-6751-2_8

  • Publisher Name: Birkhäuser Boston

  • Print ISBN: 978-1-4684-6753-6

  • Online ISBN: 978-1-4684-6751-2

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