Approximation of Sojourn Times of Gaussian Processes

We investigate the tail asymptotic behavior of the sojourn time for a large class of centered Gaussian processes $X$, in both continuous- and discrete-time framework. All results obtained here are new for the discrete-time case. In the continuous-time case, we complement the investigations of [1,2] for non-stationary $X$. A by-product of our investigation is a new representation of Pickands constant which is important for Monte-Carlo simulations and yields a sharp lower bound for Pickands constant.