Central limit theorems for the excursion set volumes of weakly dependent random fields

Abstract

The multivariate central limit theorems (CLT) for the volumes of excursion sets of stationary quasiassociated random fields on ℝ d are proved. Special attention is paid to Gaussian and shot noise fields. Formulae for the covariance matrix of the limiting distribution are provided. A statistical version of the CLT is considered as well. Some numerical results are also discussed. © 2012 ISI/BS.