On the infimum attained by the reflected fractional Brownian motion

Let {B-H (sic) : t >= 0 lozenge be a fractional Brownian motion with Hurst parameter H is an element of(1/2(c) 1). For the storage process Q(BH) (sic) = sup-infinity <= s <= t (sic)(H) (sic) B-H (sic) c (sic) s (sic) we show that, for any T (sic) > 0 such that T (sic) = O (u(2H-1/H)), P (inf(s is an element of(sic)cT(sic)) Q(BH) (sic) u) similar to P (Q(BH) (sic) u)(c) as u -> infinity This finding, known in the literature as the strong Piterbarg property, goes in line with previously observed properties of storage processes with self-similar and infinitely divisible input without Gaussian component.