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Multifractal analysis based on p-exponents and lacunarity exponents

Abstract : Many examples of signals and images cannot be modeled by locally bounded functions, so that the standard multifractal analysis, based on the H\"older exponent, is not feasible. We present a multifractal analysis based on another quantity, the p-exponent, which can take arbitrarily large negative values. We investigate some mathematical properties of this exponent, and show how it allows us to model the idea of "lacunarity" of a singularity at a point. We finally adapt the wavelet based multifractal analysis in this setting, and we give applications to a simple mathematical model of multifractal processes: Lacunary wavelet series.
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Submitted on : Tuesday, June 30, 2015 - 6:08:03 PM
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Patrice Abry, Stéphane Jaffard, Roberto Leonarduzzi, Clothilde Melot, Herwig Wendt. Multifractal analysis based on p-exponents and lacunarity exponents. Christoph Bandt et al., Eds. Fractal Geometry and Stochastics V, 70 (Part IV), Springer International Publishing, pp.279-313, 2016, Progress in Probability, 978-3-319-18659-7. ⟨10.1007/978-3-319-18660-3_15⟩. ⟨hal-01170037⟩



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