An Erdos-R,v,sz type law of the iterated logarithm for reflected fractional Brownian motion

Let be a fractional Brownian motion with Hurst parameter H a (0,1). For the stationary storage process , t ae<yen> 0, we provide a tractable criterion for assessing whether, for any positive, non-decreasing function f, equals 0 or 1. Using this criterion we find that, for a family of functions f (p) (t), such that , for some , . Consequently, with , for p ae<yen> 0, and a.s. Complementary, we prove an Erdos-R,v,sz type law of the iterated logarithm lower bound on xi (p) (t), i.e., a.s., p > 1; a.s., p a (0,1], where h (p) (t) = (1/z (p) (t))p loglog t.