On the ruin probability for physical fractional Brownian motion

We derive the exact asymptotic behavior of the ruin probability P{X(t)>x for some t>0} for the process X(t)=∫0tξ(s) ds−ct, with respect to level x which tends to infinity. We assume that the underlying process ξ(t) is a.s. continuous stationary Gaussian with mean zero and correlation function regularly varying at infinity with index −a∈(−1,0).