Multifractal analysis based on weak scaling exponent

Multifractal analysis based on the Hölder or p-exponent presupposes that the data belong to L∞ or Lp (or to Hp if p < 1). This condition is not always true. If we don’t want to regularize the data by fractional integration, we can perform a multifractal analysis based on the weak scaling exponent, which does not presuppose any regularity for the data, and can be used in the context of temperate distributions. In this prospective work, we propose multi-resolution quantities adapted to this exponent in order to investigate the numerical feasibility of the method and we show its relevance for white Gaussian noise, for which no p-exponent can be used, and we apply it on the cadence of marathon runners.