The contribution of wavelets in multifractal analysis

Stéphane Jaffard (1) , Patrice Abry (2) , Stéphane G. Roux (2) , Béatrice Vedel (1, 2) , Herwig Wendt (2)

1 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées
2 Phys-ENS - Laboratoire de Physique de l'ENS Lyon

We show how wavelet techniques allow to derive irregularity properties of functions on two particular examples: Lacunary Fourier series and some Gaussian random processes. Then, we work out a general derivation of the multifractal formalism in the sequence setting, and derive some of its properties.

Keywords: Wavelet leaders; Multifractal formalism

Domains: Computer Science [cs]; Signal and Image Processing; Engineering Sciences [physics]; Signal and Image processing

Stéphane Jaffard, Patrice Abry, Stéphane G. Roux, Béatrice Vedel, Herwig Wendt. The contribution of wavelets in multifractal analysis. The Zuhai Conference on Wavelets and Applications, Jul 2007, Zuhai, China. ⟨ensl-00354520⟩