Random wavelet series
type: Item
instance of: scholarly article
title: Random wavelet series
zbMATH Open document ID: 1011.42025
author: Jean-Marie Aubry
author: Stéphane Jaffard
published in: Communications in Mathematical Physics
publication date: 2003-03-27T00:00:00Z
review text: This paper concerns the study of functions which are known through the statistics of their wavelet coefficients. We first obtain sharp bounds on spectra of singularities and spectra of oscillating singularities, which are deduced from the sole knowledge of the wavelet histograms. Then we study a mathematical model which has been considered both in the contexts of turbulence and signal processing: random wavelet series, obtained by picking independently wavelet coefficients at each scale, following a given sequence of probability laws. The sample paths of the processes thus constructed are almost surely multifractal functions, and their spectrum of singularities and their spectrum of oscillating singularities are determined. The bounds obtained in the first part are optimal, since they become equalities in the case of random wavelet series. This allows to derive a new multifractal formalism which has a wider range of validity than those that were previously proposed in the context of fully developed turbulence.
Mathematics Subject Classification ID: 42C40
Mathematics Subject Classification ID: 94A12
Mathematics Subject Classification ID: 76F99
Mathematics Subject Classification ID: 60G17
zbMATH DE Number: 1889114
zbMATH Keywords: wavelet coefficients
zbMATH Keywords: oscillating singularities
zbMATH Keywords: turbulence
zbMATH Keywords: sample paths
zbMATH Keywords: multifractal functions
zbMATH Keywords: spectrum
zbMATH Keywords: random wavelet series
MaRDI profile type: Publication
full work available at URL: s002200200630
OpenAlex ID: W2086977223
DOI: 10.1007/S002200200630
description: scientific article; zbMATH DE number 1889114