On probability of high extremes of Gaussian fields with a smooth random trend

Publication date: Available online 1 December 2018Source: Statistics & Probability LettersAuthor(s): Goran Popivoda, Siniša StamatovićAbstractLet ξ1≔ξ1(t),t∈Rn be a centered locally ((E,α),Dt)-stationary Gaussian field, ξ2≔ξ2(t),t∈Rn be a centered differentiable in mean-square sense Gaussian field and η≔η(t),t∈Rn particular smooth random field, being independent of ξi, i=1,2. In this paper we discuss the asymptotics of Psupt∈Mk(ξi(t)+η(t))>u,asu→∞, where Mk⊂Rn is a smooth k-dimensional compact manifold, 0<k≤n, i=1,2.

Source: Statistics and Probability Letters - December 2, 2018 Category: Statistics Source Type: research