Local self-similarity and the Hausdorff dimension

Albert Benassi; Serge Cohen; Jacques Istas

doi:10.1016/S1631-073X(03)00015-3

Probability Theory

Local self-similarity and the Hausdorff dimension
[Auto-similarité locale et dimension de Hausdorff]

Présenté par : Yves Meyer

Albert Benassi ¹ ; Serge Cohen ² ; Jacques Istas ³

¹ Université Blaise Pascal (Clermont-Ferrand II), LaMP, CNRS UPRESA 6016, 63177 Aubière cedex, France
² Université Paul Sabatier, UFR MIG, Laboratoire de statistique et de probabilités, 118, route de Narbonne, 31062 Toulouse, France
³ Département IMSS, BSHM, Université Pierre Mendès-France, 38000 Grenoble, France

Comptes Rendus. Mathématique, Volume 336 (2003) no. 3, pp. 267-272.

Résumé
Abstract

Soit X un processus stochastique localement auto-similaire d'exposant 0<H<1 dont les trajectoires sont p.s. C^H−ε pour tout ε>0. Alors la dimension de Hausdorff du graphe de X est p.s. 2−H.

Let X be a locally self-similar stochastic process of index 0<H<1 whose sample paths are a.s. C^H−ε for all ε>0. Then the Hausdorff dimension of the graph of X is a.s. 2−H.

Reçu le : 2002-06-15
Accepté le : 2002-12-16
Publié le : 2003-02-01

DOI : 10.1016/S1631-073X(03)00015-3

Affiliations des auteurs :

Albert Benassi ¹ ; Serge Cohen ² ; Jacques Istas ³

¹ Université Blaise Pascal (Clermont-Ferrand II), LaMP, CNRS UPRESA 6016, 63177 Aubière cedex, France
² Université Paul Sabatier, UFR MIG, Laboratoire de statistique et de probabilités, 118, route de Narbonne, 31062 Toulouse, France
³ Département IMSS, BSHM, Université Pierre Mendès-France, 38000 Grenoble, France

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Albert Benassi; Serge Cohen; Jacques Istas. Local self-similarity and the Hausdorff dimension. Comptes Rendus. Mathématique, Volume 336 (2003) no. 3, pp. 267-272. doi : 10.1016/S1631-073X(03)00015-3. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(03)00015-3/

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