[Auto-similarité locale et dimension de Hausdorff]
Soit X un processus stochastique localement auto-similaire d'exposant 0<H<1 dont les trajectoires sont p.s. CH−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. CH−ε for all ε>0. Then the Hausdorff dimension of the graph of X is a.s. 2−H.
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@article{CRMATH_2003__336_3_267_0,
author = {Benassi, Albert and Cohen, Serge and Istas, Jacques},
title = {Local self-similarity and the {Hausdorff} dimension},
journal = {Comptes Rendus. Math\'ematique},
pages = {267--272},
publisher = {Elsevier},
volume = {336},
number = {3},
year = {2003},
doi = {10.1016/S1631-073X(03)00015-3},
language = {en},
url = {http://www.numdam.org/articles/10.1016/S1631-073X(03)00015-3/}
}
TY - JOUR AU - Benassi, Albert AU - Cohen, Serge AU - Istas, Jacques TI - Local self-similarity and the Hausdorff dimension JO - Comptes Rendus. Mathématique PY - 2003 SP - 267 EP - 272 VL - 336 IS - 3 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/S1631-073X(03)00015-3/ DO - 10.1016/S1631-073X(03)00015-3 LA - en ID - CRMATH_2003__336_3_267_0 ER -
%0 Journal Article %A Benassi, Albert %A Cohen, Serge %A Istas, Jacques %T Local self-similarity and the Hausdorff dimension %J Comptes Rendus. Mathématique %D 2003 %P 267-272 %V 336 %N 3 %I Elsevier %U http://www.numdam.org/articles/10.1016/S1631-073X(03)00015-3/ %R 10.1016/S1631-073X(03)00015-3 %G en %F CRMATH_2003__336_3_267_0
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://www.numdam.org/articles/10.1016/S1631-073X(03)00015-3/
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