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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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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DOI: https://doi.org/10.1007/s00440-011-0340-0
Keywords
- Lévy random fields
- Multifractal analysis
- Hausdorff measures and dimension
- Sets with large intersection
- Diophantine approximation
- Ubiquity