The relative multifractal analysis of a vector function in a metric space

Abstract

ABSTRACT Scale invariance is a widely used concept for analysing real data from many different applications, and multifractal analysis has become the standard and powerful tool in signal processing. It characterizes the data by globally and geometrically describing the fluctuations of the local regularity. In this paper, we study the relative vectorial multifractal formalism based on vectorial multifractal Hewitt-Stromberg measures. We use a function defined on balls in a metric space and Banach valued, which is more general than measures. This leads to results on the simultaneous behaviour of possibly many local Hölder exponents. As an application, we study the relative multifractal formalism of branching random walk on the Galton-Watson tree.