Massive excursions of Gaussian random fields. Method of moments

Asymptotic behavior of the probability of massive excursions above a high level has been evaluated for Gaussian isotropic random fields with two times a. s. differentiable trajectories. A massive excursion is an excursion which base diameter exceeds a fixed number. In order to evaluate this asymptotic behavior, a point process of exits out of a large domain is introduced for Gaussian vector field which components are copies of the initial field. Then we study the moments of this point process.
As well, general results on rough (logarithmic) asymptotic behavior of probabilities of high massive excursions are obtained.