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

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

2010-05-04

arxiv.org/abs/1005.0483v2

Bernoulli 2012, Vol. 18, No. 1, 100-118

Mathematics

Probability

Published in at http://dx.doi.org/10.3150/10-BEJ339 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statisti

Scientific paper

10.3150/10-BEJ339

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.

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