A uniform dimension result for two-dimensional fractional multiplicative processes
Annales de l'I.H.P. Probabilités et statistiques, Tome 50 (2014) no. 2, pp. 512-523.

Etant donné un processus multiplicatif fractionnaire bi-dimensionnel (F t ) t∈[0,1] déterminé par deux exposants de Hurst H 1 et H 2 , nous montrons l’existence d’un résultat uniforme pour la dimension de Hausdorff des images des sous-ensembles de [0,1] par F si et seulement si H 1 =H 2 .

Given a two-dimensional fractional multiplicative process (F t ) t∈[0,1] determined by two Hurst exponents H 1 and H 2 , we show that there is an associated uniform Hausdorff dimension result for the images of subsets of [0,1] by F if and only if H 1 =H 2 .

DOI : 10.1214/12-AIHP509
Classification : 60G18, 28A78
Mots-clés : Hausdorff dimension, fractional multiplicative processes, uniform dimension result, level sets 
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Jin, Xiong. A uniform dimension result for two-dimensional fractional multiplicative processes. Annales de l'I.H.P. Probabilités et statistiques, Tome 50 (2014) no. 2, pp. 512-523. doi : 10.1214/12-AIHP509. http://www.numdam.org/articles/10.1214/12-AIHP509/

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