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