Multivariate multifractal analysis of Levy functions. Part I: Determination of multifractal spectra

TL;DR

This paper investigates the multifractal properties of Levy functions by analyzing the Hausdorff dimensions of point sets sharing specific Hölder exponents, focusing on how these dimensions vary with translation parameters.

Contribution

It introduces a method to determine the multifractal spectra of Levy functions and examines the effect of translation on their Hausdorff dimensions.

Findings

Hausdorff dimensions depend on translation parameters

Multifractal spectra of Levy functions are characterized

Relationship between point sets and Hölder exponents established

Abstract

We study the sets of points where a L\'evy function and a translated L\'evy function share a given couple of H\''older exponents, and we investigate how their Hausdorff dimensions depend on the translation parameter.