A Functional Limit Theorem for the Integrals over Level Sets of a Gaussian Random Field

Abstract

We consider integrals of continuous random functions over random measures induced by level sets of a Gaussian random field. We show that under some conditions on the generating Gaussian field, such integrals form a continuous random process indexed by level sets. If the integrand random field possesses certain weak dependence conditions, a functional central limit theorem for those processes is proved.