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Occupation time problem for multifractional Brownian motion

Ouahra Mohamed Ait, Guerbaz Raby, Ouahhabi Hanae, Sghir Aissa

Probability and Mathematical Statistics

2019

Vol. 39, Fasc. 1

99--113

In this paper, by using a Fourier analytic approach, we investigate sample path properties of the fractional derivatives of multifractional Brownian motion local times. We also show that those additive functionals satisfy a property of local asymptotic self-similarity. As a consequence, we derive some local limit theorems for the occupation time of multifractional Brownian motion in the space of continuous functions.