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arXiv · 1005.0483

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

Alexander Bulinski·Evgeny Spodarev·Florian Timmermann
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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.

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Alexander Bulinski, Evgeny Spodarev, Florian Timmermann. 2012-03-01. Central limit theorems for the excursion set volumes of weakly dependent random fields. https://doi.org/10.3150/10-bej339

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