CLT for Excursion Sets Volumes of Random Fields

Stochastics Seminar
Thursday, April 8, 2010 - 15:00
1 hour (actually 50 minutes)
Skiles 269
Lomonosov Moscow State University
We consider various dependence concepts for random fields. Special attention is paid to Gaussian and shot-noise fields. The multivariate central limit theorems (CLT) are proved for the volumes of excursion sets of stationary quasi-associated random fields on $\mathbb{R}^d$. Formulae for the covariance matrix of the limiting distribution are provided. Statistical versions of the CLT are established as well. They employ three different estimators of the asymptotic covariance matrix. Some numerical results are also discussed.