Probability Theory
Local self-similarity and the Hausdorff dimension
[Auto-similarité locale et dimension de Hausdorff]
Comptes Rendus. Mathématique, Tome 336 (2003) no. 3, pp. 267-272.

Soit X un processus stochastique localement auto-similaire d'exposant 0<H<1 dont les trajectoires sont p.s. CHε 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. CHε for all ε>0. Then the Hausdorff dimension of the graph of X is a.s. 2−H.

Reçu le :
Accepté le :
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DOI : 10.1016/S1631-073X(03)00015-3
Benassi, Albert 1 ; Cohen, Serge 2 ; Istas, Jacques 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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Benassi, Albert; Cohen, Serge; Istas, Jacques. Local self-similarity and the Hausdorff dimension. Comptes Rendus. Mathématique, Tome 336 (2003) no. 3, pp. 267-272. doi : 10.1016/S1631-073X(03)00015-3. http://archive.numdam.org/articles/10.1016/S1631-073X(03)00015-3/

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