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Multifractal analysis of Lévy fields
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  • Published: 01 February 2011

Multifractal analysis of Lévy fields

  • Arnaud Durand1 &
  • Stéphane Jaffard2 

Probability Theory and Related Fields volume 153, pages 45–96 (2012)Cite this article

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  • 17 Citations

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Abstract

We study the pointwise regularity properties of the Lévy fields introduced by T. Mori; these fields are the most natural generalization of Lévy processes to the multivariate setting. We determine their spectrum of singularities, and we show that their Hölder singularity sets satisfy a large intersection property in the sense of K. Falconer.

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Author information

Authors and Affiliations

  1. Laboratoire de Mathématiques, UMR 8628, Université Paris-Sud, Orsay, 91405, France

    Arnaud Durand

  2. Laboratoire d’Analyse et de Mathématiques Appliquées, Université Paris-Est Créteil Val de Marne UMR 8050, 61 avenue du Général de Gaulle, Créteil, 94010, France

    Stéphane Jaffard

Authors
  1. Arnaud Durand
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  2. Stéphane Jaffard
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Correspondence to Arnaud Durand.

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Cite this article

Durand, A., Jaffard, S. Multifractal analysis of Lévy fields. Probab. Theory Relat. Fields 153, 45–96 (2012). https://doi.org/10.1007/s00440-011-0340-0

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  • Received: 17 May 2010

  • Revised: 10 December 2010

  • Published: 01 February 2011

  • Issue Date: June 2012

  • DOI: https://doi.org/10.1007/s00440-011-0340-0

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Keywords

  • Lévy random fields
  • Multifractal analysis
  • Hausdorff measures and dimension
  • Sets with large intersection
  • Diophantine approximation
  • Ubiquity

Mathematics Subject Classification (2000)

  • Primary: 60G60
  • 60G51
  • Secondary: 60G17
  • 60D05
  • 28A78
  • 28A80
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