Bernoulli

  • 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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Abstract

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.

Article information

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

Dates
First available in Project Euclid: 20 January 2012

Permanent link to this document
https://projecteuclid.org/euclid.bj/1327068619

Digital Object Identifier
doi:10.3150/10-BEJ339

Mathematical Reviews number (MathSciNet)
MR2888700

Zentralblatt MATH identifier
1239.60017

Keywords
central limit theorem dependence conditions excursion sets random fields

Citation

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. https://projecteuclid.org/euclid.bj/1327068619


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