A uniform dimension result for two-dimensional fractional multiplicative processes

Jin, Xiong

Jin, Xiong

Annales de l'I.H.P. Probabilités et statistiques, Tome 50 (2014), p. 512-523 / Harvested from Numdam

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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 $H_{1} = H_{2}$ .

Publié le : 2014-01-01

MR 3189082 | Zbl 1292.60049

DOI : https://doi.org/10.1214/12-AIHP509
Classification: 60G18, 28A78

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     author = {Jin, Xiong},
     title = {A uniform dimension result for two-dimensional fractional multiplicative processes},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     volume = {50},
     year = {2014},
     pages = {512-523},
     doi = {10.1214/12-AIHP509},
     mrnumber = {3189082},
     zbl = {1292.60049},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPB_2014__50_2_512_0}
}

Jin, Xiong. A uniform dimension result for two-dimensional fractional multiplicative processes. Annales de l'I.H.P. Probabilités et statistiques, Tome 50 (2014) pp. 512-523. doi : 10.1214/12-AIHP509. http://gdmltest.u-ga.fr/item/AIHPB_2014__50_2_512_0/

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