Multivariate multifractal analysis of Lévy functions

We study the sets of points where a Lévy function and a translated Lévy function share a given couple of Hölder exponents. The multivariate multifractal spectrum, i.e., the function which, for each couple, associates the Hausdorff dimension of the corresponding set, is estimated and we study its dependency on the translation parameter. Furthermore, we determine the univariate multifractal Legendre spectra and the multivariate multifractal Legendre spectra of shifted Lévy functions. This allows us to explore how the validity of the multivariate multifractal formalism depends on the shift parameter.