Hausdorff, Large Deviation and Legendre Multifractal Spectra of Lévy Multistable Processes

Abstract : We compute the Hausdorff multifractal spectrum of two versions of multistable Lévy motions. These processes extend classical Lévy motion by letting the stability exponent α evolve in time. The spectra provide a decomposition of [0, 1] into an uncountable disjoint union of sets with Hausdorff dimension one. We also compute the increments-based large deviations multifractal spectrum of the independent in-crements multistable Lévy motion. This spectrum turns out to be concave and thus coincides with the Legendre multifractal spectrum, but it is different from the Haus-dorff multifractal spectrum. The independent increments multistable Lévy motion thus provides an example where the strong multifractal formalism does not hold.
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https://hal.inria.fr/hal-01089482
Contributor : Ronan Le Guével <>
Submitted on : Monday, December 1, 2014 - 6:25:00 PM
Last modification on : Thursday, April 25, 2019 - 11:10:58 AM
Document(s) archivé(s) le : Monday, March 2, 2015 - 1:37:46 PM

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  • HAL Id : hal-01089482, version 1
  • ARXIV : 1412.0599

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Ronan Le Guével, Jacques Lévy Véhel. Hausdorff, Large Deviation and Legendre Multifractal Spectra of Lévy Multistable Processes. 2014. ⟨hal-01089482⟩

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