Abstract
Let { B H ( t), t ⩾ 0} be a fractional Brownian motion with index 0 < H < 1 and define the statistic V T = sup 0⩽s⩽T−a T β T|B H(s + a T) − B H(s)| , where β T and α T are suitably chosen functions of T ⩾ 0. We establish some laws of the iterated logarithm for V T .
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