Limit theorems for excursion sets of subordinated Gaussian random fields with long-range dependence

Vitalii Makogin; Evgeny Spodarev

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arXiv · 2008.00761

Limit theorems for excursion sets of subordinated Gaussian random fields with long-range dependence

Vitalii Makogin·Evgeny Spodarev

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Abstract

This paper considers the asymptotic behaviour of volumes of excursion sets of subordinated Gaussian random fields with (possibly) infinite variance. Actually, we consider integral functionals of such fields and obtain their limiting distribution using the Hermite expansion of the integrand. We consider the general non-stationary Gaussian random fields, including stationary and anisotropic special cases. The limiting random variables in our limit theorems have the form of multiple Wiener-It\^{o} integrals. We illustrate most results with corresponding examples.

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Vitalii Makogin, Evgeny Spodarev. 2020-08-03. Limit theorems for excursion sets of subordinated Gaussian random fields with long-range dependence. https://arxiv.org/abs/2008.00761

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