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Singularity sets of Lévy processes
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  • Published: 09 January 2008

Singularity sets of Lévy processes

  • Arnaud Durand1 nAff2 

Probability Theory and Related Fields volume 143, pages 517–544 (2009)Cite this article

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  • 16 Citations

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Abstract

We completely describe the size and large intersection properties of the Hölder singularity sets of Lévy processes. We also study the set of times at which a given function cannot be a modulus of continuity of a Lévy process. The Hölder singularity sets of the sample paths of certain random wavelet series are investigated as well.

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Author information

Author notes
  1. Arnaud Durand

    Present address: Applied and Computational Mathematics, California Institute of Technology, MC 217-50, Pasadena, CA, 91125, USA

Authors and Affiliations

  1. Laboratoire d’Analyse et de Mathématiques Appliquées, Université Paris XII, 61 avenue du Général de Gaulle, 94010, Créteil Cedex, France

    Arnaud Durand

Authors
  1. Arnaud Durand
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Correspondence to Arnaud Durand.

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Cite this article

Durand, A. Singularity sets of Lévy processes. Probab. Theory Relat. Fields 143, 517–544 (2009). https://doi.org/10.1007/s00440-007-0134-6

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  • Received: 23 April 2007

  • Revised: 12 December 2007

  • Published: 09 January 2008

  • Issue Date: March 2009

  • DOI: https://doi.org/10.1007/s00440-007-0134-6

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Keywords

  • Lévy processes
  • Random wavelet series
  • Multifractal analysis
  • Sets with large intersection and Hausdorff measures
  • Ubiquity

Mathematics Subject Classification (2000)

  • Primary: 60D05
  • Secondary: 60G51
  • 60G17
  • 26A15
  • 28A80
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