Multiparameter multifractional brownian motion : local nondeterminism and joint continuity of the local times
Annales de l'I.H.P. Probabilités et statistiques, Volume 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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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, Volume 47 (2011) no. 4, pp. 1029-1054. doi : 10.1214/10-AIHP408. http://www.numdam.org/articles/10.1214/10-AIHP408/

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