Multivariate multifractal analysis of L{\'e}vy functions. Part II: Validity of the multifractal formalism

TL;DR

This paper investigates the validity of the multivariate multifractal formalism for shifted Lévy functions by analyzing their Legendre spectra and how this validity depends on the shift parameter.

Contribution

It extends previous work by exploring the multivariate multifractal spectra of Lévy functions and examining the impact of shift parameters on the formalism's validity.

Findings

Multivariate multifractal spectra of shifted Lévy functions are determined.

The validity of the multifractal formalism depends on the shift parameter.

Extension of previous bivariate analysis to multivariate case.

Abstract

In this article, we determine the multivariate multifractal Legendre spectra of shifted L{\'e}vy functions. This allows us to explore how the validity of the multivariate multifractal formalism depends on the shift parameter. This article is a continuation of [10] where the corresponding bivariate multifractal spectra were explored.