Approximation of Sojourn Times of Gaussian Processes

Abstract

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.

26 pages

References in corpus (1)

• Maxima of asymptotically Gaussian random fields and moderate deviation approximations to boundary crossing probabilities of sums of random variables with multidimensional indices

Cited by in corpus (1)

• On generalized Piterbarg-Berman function