Annales de l'Institut Henri Poincaré, Probabilités et Statistiques

Multiparameter multifractional Brownian motion: Local nondeterminism and joint continuity of the local times

Antoine Ayache, Narn-Rueih Shieh, and Yimin Xiao

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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.

Article information

Ann. Inst. H. Poincaré Probab. Statist., Volume 47, Number 4 (2011), 1029-1054.

First available in Project Euclid: 6 October 2011

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Zentralblatt MATH identifier

Primary: 60G15: Gaussian processes 60G17: Sample path properties 28A80: Fractals [See also 37Fxx]

Multifractional Brownian motion Local nondeterminism Local times Joint continuity


Ayache, Antoine; Shieh, Narn-Rueih; Xiao, Yimin. Multiparameter multifractional Brownian motion: Local nondeterminism and joint continuity of the local times. Ann. Inst. H. Poincaré Probab. Statist. 47 (2011), no. 4, 1029--1054. doi:10.1214/10-AIHP408.

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