A limit theorem for the time of ruin in a Gaussian ruin problem

For certain Gaussian processes X(t)X(t) with trend −ctβ−ctβ and variance V2(t)V2(t), the ruin time is analyzed where the ruin time is defined as the first time point tt such that X(t)−ctβ≥uX(t)−ctβ≥u. The ruin time is of interest in finance and actuarial subjects. But the ruin time is also of interest in other applications, e.g. in telecommunications where it indicates the first time of an overflow. We derive the asymptotic distribution of the ruin time as u→∞u→∞ showing that the limiting distribution depends on the parameters ββ, V(t)V(t) and the correlation function of X(t)X(t).