Sample path properties of the local time of multifractional Brownian motion

Abstract

We establish estimates for the local and uniform moduli of continuity of the local time of multifractional Brownian motion, $B^H=(B^{H(t)}(t),t\in\mathbb{R}^+)$. An analogue of Chung's law of the iterated logarithm is studied for $B^H$ and used to obtain the pointwise Hölder exponent of the local time. A kind of local asymptotic self-similarity is proved to be satisfied by the local time of $B^H$.