Variation totale multivariee pour la detection de changement du spectre multifractal
In essence, practical multifractal analysis a priori assumes that the multifractal properties of signals are homogeneous, i.e., do not vary along time. We are interested here in situations of practical relevance where multifractal properties may change along time. Variational, or optimization, univariate and multivariate procedures are developed that aim to detect such changes in multifractal properties. They rely on the use of total variation and mixed norms. Univariate and multivariate approaches are compared using several performance criteria applied topiece-wise homogeneous multifractal processes.