A review of univariate and multivariate multifractal analysis illustrated by the analysis of marathon runners physiological data

2022/09/29 by Stéphane Jaffard, Jaffard, Stéphane, Guillaume Saës +7 · 2 citations
Computer Science · Economics, Econometrics and Finance · #Classical Analysis and ODEs (math.CA) #Complex Systems and Time Series Analysis #FOS: Biological sciences #FOS: Electrical engineering #FOS: Mathematics #Functional Analysis (math.FA) #Signal Processing (eess.SP) #Time Series Analysis and Forecasting #Tissues and Organs (q-bio.TO) #electronic engineering #information engineering

paper · doi:10.48550/arxiv.2209.14612

openalex publication_date 2022/09/29 · openalex created_date 2023/05/28 · openalex updated_date 2026/07/28

Abstract

We review the central results concerning wavelet methods in multifractal analysis, which consists in analysis of the pointwise singularities of a signal, and we describe its recent extension to multivariate multifractal analysis, which deals with the joint analysis of several signals; we focus on the mathematical questions that this new techniques motivate. We illustrate these methods by an application to data recorded on marathon runners.

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