A central limit theorem for Lebesgue integrals of random fields

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.

arXiv comment10 pages