Construction et étude de quelques processus multifractals

Abstract : Since their emergence in the 80's in the areas of turbulence and of strange attractors, multifractals have gained popularity. They appear now in finance, geophysics, study of network traffic and in many other areas of applied sciences. This development required adapted theoretical models. Bacry and Muzy's Multifractal Random Measure is one of these models. Thanks to its generality, its flexibility and to its relative simplicity, it became central in the domain of multifractals over the past ten years. In this PhD thesis, two families of multifractal processes are proposed. Their construction is based on the works of Schmitt and co-authors and of those of Bacry and Muzy. After the introduction (chapter 1), we use in chapter 2 alpha-stable moving averages to build multifractal processes; whereas chapter 3 is devoted to the construction of Multifractal Fractional Random Walks with Hurst index 0
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Contributor : Nicolas Perpète <>
Submitted on : Sunday, December 1, 2013 - 8:54:41 PM
Last modification on : Tuesday, July 3, 2018 - 11:42:11 AM
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N. Perpète. Construction et étude de quelques processus multifractals. Probabilités [math.PR]. Université des Sciences et Technologie de Lille - Lille I, 2013. Français. ⟨tel-00912273⟩

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