2024/11/21 by Stéphane Seuret, Seuret, Stéphane
Economics, Econometrics and Finance · #Complex Systems and Time Series Analysis #FOS: Mathematics #Metric Geometry (math.MG)
paper · pdf · doi:10.48550/arxiv.2411.13959
openalex publication_date 2024/11/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
In this article, we investigate the bivariate multifractal analysis of pairs of Borel probability measures. We prove that, contrarily to what happens in the univariate case, the natural extension of the Legendre spectrum does not yield an upper bound for the bivariate multifractal spectrum. For this we build a pair of measures for which the two spectra have disjoint supports. Then we study the bivariate multifractal behavior of an archetypical pair of randomly correlated measures, which give new, surprising, behaviors, enriching the narrow class of measures for which such an analysis is achieved.