The time of ultimate recovery in Gaussian risk model

We analyze the distance RT(u) between the first and the last passage time of {X(t) - ct : t is an element of [0, T]} at level u in time horizon T is an element of (0, infinity], where X is a centered Gaussian process with stationary increments and c is an element of, given that the first passage time occurred before T. Under some tractable assumptions on X, we find Delta(u) and G(x) such that limu ->infinity RT(u)>Delta(u)x-formula> for x >= 0. We distinguish two scenarios: T < infinity and T = infinity, that lead to qualitatively different asymptotics. The obtained results provide exact asymptotics of the ultimate recovery time after the ruin in Gaussian risk model.