Limit Theorems for Excursion Sets of Stationary Random Fields

Evgeny Spodarev ()
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Evgeny Spodarev: Ulm University

A chapter in Modern Stochastics and Applications, 2014, pp 221-241 from Springer

Abstract: Abstract We give an overview of the recent asymptotic results on the geometry of excursion sets of stationary random fields. Namely, we cover a number of limit theorems of central type for the volume of excursions of stationary (quasi-, positively or negatively) associated random fields with stochastically continuous realizations for a fixed excursion level. This class includes in particular Gaussian, Poisson shot noise, certain infinitely divisible, α-stable, and max-stable random fields satisfying some extra dependence conditions. Functional limit theorems (with the excursion level being an argument of the limiting Gaussian process) are reviewed as well. For stationary isotropic C 1-smooth Gaussian random fields similar results are available also for the surface area of the excursion set. Statistical tests of Gaussianity of a random field which are of importance to real data analysis as well as results for an increasing excursion level round up the paper.

Keywords: Limit Theorem; Random Field; Gaussian Process; Gaussian Random Field; Functional Central Limit Theorem (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-3-319-03512-3_13

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DOI: 10.1007/978-3-319-03512-3_13

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