The singularity spectrum of Lévy processes in multifractal time |
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Authors: | Julien Barral,Sté phane Seuret |
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Affiliation: | a Projet SISYPHE, INRIA, Domaine de Voluceau Rocquencourt, 78153 Le Chesnay cedex, France b Laboratoire d'Analyse et de Mathématiques Appliquées, Faculté de Sciences et Technologie, 61, avenue du Général de Gaulle, 94010 Créteil cedex, France |
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Abstract: | Let X=(Xt)t?0 be a Lévy process and μ a positive Borel measure on R+. Suppose that the integral of μ defines a continuous increasing multifractal time . Under suitable assumptions on μ, we compute the singularity spectrum of the sample paths of the process X in time μ defined as the process (XF(t))t?0.A fundamental example consists in taking a measure μ equal to an “independent random cascade” and (independently of μ) a suitable stable Lévy process X. Then the associated process X in time μ is naturally related to the so-called fixed points of the smoothing transformation in interacting particles systems.Our results rely on recent heterogeneous ubiquity theorems. |
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Keywords: | 60Gxx 28A78 28A80 28C15 |
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