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 quasi-associated random fields on ${\mathbb{R}}^d$ 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.

Published in at http://dx.doi.org/10.3150/10-BEJ339 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)

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