A functional central limit theorem for integrals of stationary mixing random fields

Abstract

We prove a functional central limit theorem for integrals ${\int }_{W}f(X(t))dt$, where $(X(t){)}_{t\in {\mathbb{R}}^d}$ 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.

arXiv comment14 pages, 1 figure