Multivariate multifractal analysis of Lévy functions. Part II: Validity of the multifractal formalism

2025/05/14 by Stéphane Jaffard, Jaffard, Stéphane, Lingmin Liao +3 · 1 citation
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Complex Systems and Time Series Analysis #Mathematical Dynamics and Fractals #Chaos control and synchronization

paper · pdf · doi:10.48550/arxiv.2505.09230

Abstract

In this article, we determine 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. This article is a continuation of [10] where the corresponding bivariate multifractal spectra were explored.

Citations

• Multivariate multifractal analysis of Levy functions. Part I: Determination of multifractal spectra
• On the multivariate multifractal formalism: examples and counter-examples
• A review of univariate and multivariate multifractal analysis illustrated by the analysis of marathon runners physiological data
• Irregularities and Scaling in Signal and Image Processing: Multifractal\n Analysis

Cited by

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

Related

• Multivariate multifractal analysis of Levy functions. Part I: Determination of multifractal spectra
• Revisiting multifractal analysis
• On the multivariate multifractal formalism: examples and counter-examples
• Fine and coarse multifractal zeta-functions: On the multifractal formalism for multifractal zeta-functions
• Hausdorff, Large Deviation and Legendre Multifractal Spectra of Lévy Multistable Processes