Hausdorff, Large Deviation and Legendre Multifractal Spectra of L\'evy Multistable Processes

Autor:	Guével, Ronan Le, Véhel, Jacques Lévy
Rok vydání:	2014
Předmět:	Mathematics - Probability
Druh dokumentu:	Working Paper
Popis:	We compute the Hausdorff multifractal spectrum of two versions of multistable L{\'e}vy motions. These processes extend classical L{\'e}vy motion by letting the stability exponent $\alpha$ 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 L{\'e}vy 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 L{\'e}vy motion thus provides an example where the strong multifractal formalism does not hold.
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1412.0599 Zobrazit plný text záznamu View this record from Arxiv