Abstract: 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.

2000 AMS Mathematics Subject Classification: Primary: 60F25, 60J55; Secondary: 60G22.

Keywords and phrases: Local time, local asymptotic self-similarity, limit theorem, fractional Brownian motion, multifractional Brownian motion, fractional derivative.