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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.

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