We prove a functional central limit theorem for integrals W f (X(t)) dt, where (X(t)) t∈R d is a stationary mixing random field and the stochastic process is indexed by the function f , as the integration domain W grows in Van Hove-sense. We discuss properties of the covariance function of the asymptotic Gaussian process.

In this paper we show a central limit theorem for Lebesgue integrals of stationary BL(θ)-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.