Sample Path Properties of the Local Time of Multifractional Brownian Motion

We establish estimates for the local and uniform moduli of continuity of the local time of multifractional Brownian motion, $B^{H}=(B^{H(t)}(t),t\in {\Bbb R}^{+})$ . 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 $B^{H}$ .