Multiparameter multifractional brownian motion : local nondeterminism and joint continuity of the local times
Ayache, Antoine ; Shieh, Narn-Rueih ; Xiao, Yimin
Annales de l'I.H.P. Probabilités et statistiques, Tome 47 (2011), p. 1029-1054 / Harvested from Numdam
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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.

Publié le : 2011-01-01
DOI : https://doi.org/10.1214/10-AIHP408
Classification:  60G15,  60G17,  28A80 
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     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},
     volume = {47},
     year = {2011},
     pages = {1029-1054},
     doi = {10.1214/10-AIHP408},
     zbl = {1268.60048},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPB_2011__47_4_1029_0}
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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) pp. 1029-1054. doi : 10.1214/10-AIHP408. http://gdmltest.u-ga.fr/item/AIHPB_2011__47_4_1029_0/

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