Continuous Large Deviation Multifractal Spectrum: Definition and Estimation

Abstract : The large deviation multifractal spectrum gives important statistical informations on irregular measures. However it is difficult to estimate. In this paper, we propose two new definitions of the large deviation spectrum better adapted to the design of various estimators. They rely on the computation of the Lebesgue measure of the reunion of all intervals of same size whose coarse grain Hölder exponent is equal to a Höder exponent. In particular, we introduce the continuous large deviation spectrum for which we construct different estimators. We finally show some numerical results obtained on both deterministic and random synthetical signals.
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Communication dans un congrès
M M Novak. Fractals 98, Oct 1998, Valleta, Malta. World Scientific, 1998
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  • HAL Id : inria-00592418, version 1

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Canus Christophe, Jacques Lévy Véhel, Claude Tricot. Continuous Large Deviation Multifractal Spectrum: Definition and Estimation. M M Novak. Fractals 98, Oct 1998, Valleta, Malta. World Scientific, 1998. 〈inria-00592418〉

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