Multiparameter multifractional brownian motion : local nondeterminism and joint continuity of the local times
Annales de l'I.H.P. Probabilités et statistiques, Tome 47 (2011) no. 4, pp. 1029-1054.

Au moyen d'une méthode d'ondelettes nous montrons que le mouvement Brownien multifractionnaire de type harmonisable à N indices (mfBm) est un champ gaussien localement non-déterministe. Grâce à cette propriété nous établissons ensuite la bicontinuité des temps locaux d'un (N, d)-mfBm et cela nous permet d'obtenir de nouveaux résultats concernant son comportement trajectoriel.

By using a wavelet method we prove that the harmonisable-type N-parameter multifractional brownian motion (mfBm) is a locally nondeterministic gaussian random field. This nice property then allows us to establish joint continuity of the local times of an (N, d)-mfBm and to obtain some new results concerning its sample path behavior.

DOI : https://doi.org/10.1214/10-AIHP408
Classification : 60G15,  60G17,  28A80
Mots clés : multifractional brownian motion, local nondeterminism, local times, joint continuity
@article{AIHPB_2011__47_4_1029_0,
     author = {Ayache, Antoine and Shieh, Narn-Rueih and Xiao, Yimin},
     title = {Multiparameter multifractional brownian motion : local nondeterminism and joint continuity of the local times},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     pages = {1029--1054},
     publisher = {Gauthier-Villars},
     volume = {47},
     number = {4},
     year = {2011},
     doi = {10.1214/10-AIHP408},
     zbl = {1268.60048},
     language = {en},
     url = {http://archive.numdam.org/item/AIHPB_2011__47_4_1029_0/}
}
Ayache, Antoine; Shieh, Narn-Rueih; Xiao, Yimin. Multiparameter multifractional brownian motion : local nondeterminism and joint continuity of the local times. Annales de l'I.H.P. Probabilités et statistiques, Tome 47 (2011) no. 4, pp. 1029-1054. doi : 10.1214/10-AIHP408. http://archive.numdam.org/item/AIHPB_2011__47_4_1029_0/

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