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

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 .

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 .

DOI : https://doi.org/10.1214/12-AIHP509
Classification:  60G18,  28A78
Keywords: Hausdorff dimension, fractional multiplicative processes, uniform dimension result, level sets
@article{AIHPB_2014__50_2_512_0,
     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},
     publisher = {Gauthier-Villars},
     volume = {50},
     number = {2},
     year = {2014},
     pages = {512-523},
     doi = {10.1214/12-AIHP509},
     zbl = {1292.60049},
     mrnumber = {3189082},
     language = {en},
     url = {http://www.numdam.org/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, Volume 50 (2014) no. 2, pp. 512-523. doi : 10.1214/12-AIHP509. http://www.numdam.org/item/AIHPB_2014__50_2_512_0/

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