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Intersection Exponents and the Multifractal Spectrum for Measures on Brownian Paths

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Fractal Geometry and Stochastics III

Part of the book series: Progress in Probability ((PRPR,volume 57))

Abstract

The aim of this paper is to give a survey of recent developments in the multifractal analysis of measures arising in the study of Brownian motion. We first discuss the harmonic measure on a Brownian path, studied by Lawler, and the intersection local time on the intersection of two independent Brownian paths, studied by Klenke and Morters. In both examples the intersection exponents of Brownian motion play a crucial role in the multifractal analysis. Whereas the first example is in line with the multifractal formalism, the second example is not and more subtle effects come into the picture. Then we discuss the occupation measure of Brownian motion, in which case a refined multifractal analysis was carried out by Dembo, Peres, Rosen and Zeitouni.

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Authors and Affiliations

  1. Department of Mathematical Sciences, University of Bath, Claverton Down, Bath BA2 6PA, UK

    Peter Mörters

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  1. Peter Mörters
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Editors and Affiliations

  1. Institut für Mathematik und Informatik, Ernst-Moritz-Arndt-Universität, Greifswald, 17487, Germany

    Christoph Bandt

  2. Department of Physics, University of Rome La Sapienza, Via G. Boni 20, Roma, 00162, Italy

    Umberto Mosco

  3. Mathematisches Institut, Friedrich-Schiller-Universität, Jena, 07740, Germany

    Martina Zähle

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Mörters, P. (2004). Intersection Exponents and the Multifractal Spectrum for Measures on Brownian Paths. In: Bandt, C., Mosco, U., Zähle, M. (eds) Fractal Geometry and Stochastics III. Progress in Probability, vol 57. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7891-3_9

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  • DOI: https://doi.org/10.1007/978-3-0348-7891-3_9

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9612-2

  • Online ISBN: 978-3-0348-7891-3

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