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Quelques notions d'irrégularité uniforme et ponctuelle : le point de vue ondelettes

Abstract : The main purpose of this thesis is the definition and the study of different concepts of uniform or pointwise irregularity which enable one to account for the fact that a function may have 'large increments' at any scales. To this end, we 'invert' the usual notions of Hölderian regularity. The main goal is then to relate these different concepts to wavelet theory. The wavelet criteria supplied enable to define functions or random fields the behavior of which differ with respect the family of scales chosen. Moreover, if we consider the pointwise point of view, a natural question is that of the definition of a weak multifractal analysis related to pointwise irregularity. Finally, we study examples of random fields with some properties of directional regularity. Thus we focus on the study of a special model of operator scaling Gaussian field. We then extend this model and introduced group self-similar Gaussian fields
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Submitted on : Monday, March 8, 2010 - 5:21:19 PM
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Marianne Clausel. Quelques notions d'irrégularité uniforme et ponctuelle : le point de vue ondelettes. Mathématiques générales [math.GM]. Université Paris-Est, 2008. Français. ⟨NNT : 2008PEST0062⟩. ⟨tel-00462162⟩



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