• Bernoulli
  • Volume 18, Number 1 (2012), 100-118.

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

Alexander Bulinski, Evgeny Spodarev, and Florian Timmermann

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The multivariate central limit theorems (CLT) for the volumes of excursion sets of stationary quasi-associated random fields on ℝd 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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Bernoulli, Volume 18, Number 1 (2012), 100-118.

First available in Project Euclid: 20 January 2012

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central limit theorem dependence conditions excursion sets random fields


Bulinski, Alexander; Spodarev, Evgeny; Timmermann, Florian. Central limit theorems for the excursion set volumes of weakly dependent random fields. Bernoulli 18 (2012), no. 1, 100--118. doi:10.3150/10-BEJ339.

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