School Seminars and Colloquia

Multifractal Analysis : the wavelet leaders contribution


by Patrice Abry

Institution: CNRS, Laboratoire de Physique, Ecole Normale Supérieure de Lyon
Date: Fri 24th November 2006
Time: 3:15 PM
Location: Theatre 2, Ground Floor, 111 Barry Street, Carlton

Abstract: The properties of several multifractal formalisms based on wavelet coefficients are compared from both mathematical and numerical points of view. When it is based directly on wavelet coefficients, the multifractal formalism is shown to yield, at best, the increasing part of the weak scaling exponent spectrum. The formalism has to be based on new multiresolution quantities, the wavelet leaders, in order to yield the entire and correct spectrum of Hölder singularities. The properties of this new multifractal formalism and of the alternative weak scaling exponent multifractal formalism are investigated. Examples based on known synthetic multifractal processes illustrate its numerical implementation and abilities. The benefits of the use of wavelet leaders is also illustrated on actual empirical data coming from hydrodynamics turbulence experiments.(Joint work with S. Jaffard, Dept. of Mathematics, Université Paris XII, Creteil France)

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