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Analysis of multifractal signals

Stephane Jaffard
University of Paris XII

Large classes of signals exhibit a very irregular behavior. In the most complicated situations, this irregular behavior may follow different regimes, and can switch from one regime to another almost instantaneously. Such signals cannot be modelled by standard stationary increments processes, such as Fractional Brownian Motions (or related gaussian processes) for instance. The techniques of multifractal signal analysis have been specifically designed to analyze such behaviors. Initially developed in the mid 80's in the context of turbulence analysis, they were applied successfully to a large range of signals, including traffic data (cars and internet!), stock market prices, speech signals, texture analysis of images, ... We will give an overview of the mathematical tools that were developed for that purpose (Holder regularity, Spectrum of singularities, thermodynamic formalism, chirps and oscillating singularities), and we will present some of the most successful applications.

Stephane Jaffard was born on May 23, 1962 at Boulogne-Billancourt. He has been a Professor of Mathematics at Universite Paris XII-Val de Marne since September 1, 1995. He graduated from the Ecole Polytechnique in 1984 and did his PhD in 1989 under Yves Meyer (Member of the French Academy of Sciences) on the topic of "Construction and Properties of Wavelet Bases". In 1989-90, Stephane was a Member of the Institute for Advanced Study (Princeton)

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