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November 2011 Multiparameter multifractional Brownian motion: Local nondeterminism and joint continuity of the local times
Antoine Ayache, Narn-Rueih Shieh, Yimin Xiao
Ann. Inst. H. Poincaré Probab. Statist. 47(4): 1029-1054 (November 2011). DOI: 10.1214/10-AIHP408

Abstract

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.

Citation

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Antoine Ayache. Narn-Rueih Shieh. Yimin Xiao. "Multiparameter multifractional Brownian motion: Local nondeterminism and joint continuity of the local times." Ann. Inst. H. Poincaré Probab. Statist. 47 (4) 1029 - 1054, November 2011. https://doi.org/10.1214/10-AIHP408

Information

Published: November 2011
First available in Project Euclid: 6 October 2011

zbMATH: 1268.60048
MathSciNet: MR2884223
Digital Object Identifier: 10.1214/10-AIHP408

Subjects:
Primary: 28A80, 60G15, 60G17

Rights: Copyright © 2011 Institut Henri Poincaré

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Vol.47 • No. 4 • November 2011
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