no. 4
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

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.

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.

DOI : 10.1214/10-AIHP408
Classification : 60G15, 60G17, 28A80
Keywords: multifractional brownian motion, local nondeterminism, local times, joint continuity 
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     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
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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) no. 4, pp. 1029-1054. doi: 10.1214/10-AIHP408

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