On first and last ruin times of Gaussian processes

Considering centered Gaussian processes X(t)X(t) with a trend −ctβ−ctβ and variance V2(t)V2(t), we are interested in the asymptotic distributions of the first ruin time and the last ruin time as well as their joint asymptotic distribution as the initial capital u→∞u→∞. Our results show that the conditional distribution of the last ruin time, conditioned on ruin occurring, is a normal distribution and the conditional joint limit distribution is a difference of two standard normal distributions.