Sample path properties of the local time of multifractional Brownian motion

Brahim Boufoussi (1) , Marco Dozzi (2) , Raby Guerbaz (1)

1 Faculté des Sciences Semlalia [Marrakech]
2 IECN - Institut Élie Cartan de Nancy

Estimates for the local and uniform moduli of continuity of the local time of the multifractional Brownian motion (mBm) are given. An analog of the Chung law of the iterated logarithm is studied for mBm and used to obtain the pointwise Hölder exponent of its local time. Local asymptotic selfsimilarity is proved to be satisfied by the local time of mBm and a limit theorem for occupation integrals is given.

Mots clés: Chung-type law of iterated logarithm; local asymptotic self-similarity; multifractional Brownian motion; local times

Domaines: Probabilités [math.PR]

Brahim Boufoussi, Marco Dozzi, Raby Guerbaz. Sample path properties of the local time of multifractional Brownian motion. Bernoulli, 2007, 13 (3), pp.849-867. ⟨10.3150/07-BEJ6140⟩. ⟨hal-00098675v3⟩