Extremes of locally stationary Gaussian and chi fields on manifolds

Abstract

Depending on a parameter h ∈ (0, 1], let {X h (t), t ∈ M h } be a class of centered Gaussian fields indexed by compact manifolds M h . For locally stationary Gaussian fields X h , we study the asymptotic excursion probabilities of X h on M h . Two cases are considered: (i) h is fixed and (ii) h → 0. These results are extended to obtain the limit behaviors of the extremes of locally stationary χ-fields on manifolds.