Extremes of Gaussian random fields with non-additive dependence structure

Long Bai, Krzysztof Debicki, Peng Liu

Published 2021-08-20Version 1

We derive exact asymptotics of $$\mathbb{P}\left(\sup_{t\in \mathcal{A}}X(t)>u\right), ~\text{as}~ u\to\infty,$$ for a centered Gaussian field $X(t),~t\in \mathcal{A}\subset\mathbb{R}^n$, $n>1$ with continuous sample paths a.s. and general dependence structure, for which $\arg \max_{t\in {\mathcal{A}}} Var(X(t))$ is a Jordan set with finite and positive Lebesque measure of dimension $k\leq n$. Our findings are applied to deriving the asymptotics of tail probabilities related to performance tables and dependent chi processes.