Approximation of the maximum of storage process with fractional Brownian motion as input

In this paper, the asymptotic relation between the maximum of the storage process and the maximum of the process sampled at discrete time points is studied. It is shown that these two maxima are asymptotically independent or dependent when the grids of the discrete time points are sufficiently sparse or the so-called Pickands grids. The results complete a gap in Hüsler and Piterbarg (2004) which showed that the two maxima are asymptotically coincident when the grids of the discrete time points are sufficiently dense.