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A New Multifractal Formalism, with Application to Random Wavelet Series


Speaker: Jean-Marie Aubry, UC Davis, Mathematics
Location: 693 Kerr
Start time: Mon, Jun 5 2000, 4:10PM

We propose a new multifractal formalism, based on histograms of wavelet coefficients. This new formalism yields a spectrum of H\"older and oscillating singularity exponents, and is not limited to concave spectra. We show that the corresponding upper bound holds with a minimal global regularity hypothesis. This upper bound is achieved for almost all realizations of a stochastic process called random wavelet series, obtained by drawing independently the wavelet coefficients with a general scale-dependent law.