Hausdorff, Large Deviation and Legendre Multifractal Spectra of Lévy Multistable ProcessesReport as inadecuate




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1 Regularity - Probabilistic modelling of irregularity and application to uncertainties management Inria Saclay - Ile de France 2 IRMAR - Institut de Recherche Mathématique de Rennes 3 MAS - Mathématiques Appliquées aux Systèmes - EA 4037

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.





Author: Ronan Le Guével - Jacques Lévy Véhel -

Source: https://hal.archives-ouvertes.fr/



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