2014/12/01 by Ronan Le Guével, Guével, Ronan Le, Jacques Lévy Véhel +1
Economics, Econometrics and Finance · Mathematics · #Complex Systems and Time Series Analysis #FOS: Mathematics #Financial Risk and Volatility Modeling #Mathematical Dynamics and Fractals #Probability (math.PR) #math.PR
paper · pdf · doi:10.48550/arxiv.1412.0599
arxiv created 2014/12/01 · openalex publication_date 2014/12/01 · arxiv updated 2014/12/02 · openalex created_date 2022/08/30 · openalex updated_date 2026/07/28
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.