HAL Id: inria-00592418
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Submitted on 12 May 2011
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Continuous Large Deviation Multifractal Spectrum:
Definition and Estimation
Canus Christophe, Jacques Lévy Véhel, Claude Tricot
To cite this version:
Canus Christophe, Jacques Lévy Véhel, Claude Tricot. Continuous Large Deviation Multifractal Spectrum: Definition and Estimation. Fractals 98, Oct 1998, Valleta, Malta. �inria-00592418�
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 intervals: I n measures: µn
4 first steps of preïmultifractal binomial measure of parameter: p
0=0.1 0 0.5 1 1.5 2 2.5 3 3.5 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Hoelder exponents: _ spectra: f( _ )
large deviation spectra of a binomial
0 0.5 1 1.5 2 2.5 3 3.5 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Hoelder exponents: _ spectra: f( _ )
large deviation spectra of a lumping of binomials
0 0.2 0.4 0.6 0.8 1 1.2 1.4 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Hoelder exponents: _ spectra: f( _ )
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 intervals: In measures: W n
Preïmultifractal random uniform measure (resolution n=10)
0 0.5 1 1.5 2 2.5 3 3.5 ï0.2 0 0.2 0.4 0.6 0.8 1 1.2 Hoelder exponents: _ spectra: f( _ )