Extremes of Gaussian random fields with non-additive dependence structure

2021/08/20 by Long Bai, Bai, Long, Krzysztof Dȩbicki +3
Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Financial Risk and Volatility Modeling #Primary 60G15 #Probability (math.PR) #Statistical Methods and Inference #Stochastic processes and statistical mechanics #secondary 60G70

paper · pdf · doi:10.48550/arxiv.2108.09225

openalex publication_date 2021/08/20 · openalex created_date 2021/08/30 · openalex updated_date 2026/07/28

Abstract

We derive exact asymptotics of ℙ(sup_t∈ AX(t)gt;u),~ as~ u→∞, for a centered Gaussian field X(t),~ t∈ A⊂ℝⁿ, n>1 with continuous sample paths a.s., for which arg max_t∈ A Var(X(t)) is a Jordan set with finite and positive Lebesque measure of dimension k≤ n and its dependence structure is not necessarily locally stationary. Our findings are applied to deriving the asymptotics of tail probabilities related to performance tables and chi processes where the covariance structure is not locally stationary.

Citations

• Extremes of Gaussian Random Fields with maximum variance attained over smooth curves

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