Chung's Functional Law of the Iterated Logarithm for Increments of a Fractional Brownian Motion

摘要

In this paper, we present Chung's functional law of the iterated logarithm for increments of a fractional Brownian motion. The corresponding results in Gao and Wang (Stat Probab Lett 73:165-177, 2005), Monrad and Rootzen (Probab Theory Relat Fields 101:173-192, 1995) and Wang (J Theor Probab 18(2):327-343, 2005) are extended. The main tools in the proof are large deviations and small deviations for fractional Brownian motion.