Extremes of Gaussian fields with a smooth random variance

In this paper we investigate the probabilities of large extremes P(supt∈Tξ(t)η(t)>u), as u→∞, where ξ(t) is a centered homogeneous Gaussian random field, η(t) is particular smooth field independent of ξ(t) and T⊂Rn is a closed Jordan set.