Point processes of exceedances by Gaussian random fields with applications to asymptotic locations of extreme order statistics

Abstract

In this paper, we studied the limit properties of the point processes of exceedances by stationary dependent Gaussian random fields. Applying the obtained results, we investigated the asymptotic relations between the locations and heights of extreme order statistics for stationary dependent Gaussian random fields. It is shown that these asymptotic relations are not sensitive to the dependence of the Gaussian random fields.