A uniform dimension result for two-dimensional fractional multiplicative processes

Jin, Xiong

doi:10.1214/12-AIHP509

Jin, Xiong

Annales de l'I.H.P. Probabilités et statistiques, Tome 50 (2014) no. 2, pp. 512-523.

Résumé
Abstract

Etant donné un processus multiplicatif fractionnaire bi-dimensionnel ${(F_{t})}_{t \in [0, 1]}$ 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 ${(F_{t})}_{t \in [0, 1]}$ 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 $H_{1} = H_{2}$ .

EuDML MR Zbl

DOI : 10.1214/12-AIHP509

Classification : 60G18, 28A78
Mots clés : Hausdorff dimension, fractional multiplicative processes, uniform dimension result, level sets

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     title = {A uniform dimension result for two-dimensional fractional multiplicative processes},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     pages = {512--523},
     publisher = {Gauthier-Villars},
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     number = {2},
     year = {2014},
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     url = {http://www.numdam.org/articles/10.1214/12-AIHP509/}
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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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