A central limit theorem for Lebesgue integrals of random fields

TL;DR

This paper proves a central limit theorem for Lebesgue integrals of stationary dependent random fields as the domain expands, extending known results from discrete sums to continuous integrals.

Contribution

It introduces a new CLT for Lebesgue integrals of stationary $BL(\theta)$-dependent random fields, broadening the scope of existing discrete sum results.

Findings

Established CLT for Lebesgue integrals of dependent random fields.

Extended CLT to multivariate cases.

Demonstrated applicability to various dependent structures.

Abstract

In this paper we show a central limit theorem for Lebesgue integrals of stationary $BL(\theta)$-dependent random fields as the integration domain grows in Van Hove-sense. Our method is to use the (known) analogue result for discrete sums. As applications we obtain various multivariate versions of this central limit theorem.