Extremes of vector-valued Gaussian processes: Exact asymptotics

Krzysztof Dȩbicki, Enkelejd Hashorva, Lanpeng Ji and Kamil Tabiś

Stochastic Processes and their Applications, 2015, vol. 125, issue 11, 4039-4065

Abstract: Let {Xi(t),t≥0},1≤i≤n be mutually independent centered Gaussian processes with almost surely continuous sample paths. We derive the exact asymptotics of P(∃t∈[0,T]∀i=1,…,nXi(t)>u) as u→∞, for both locally stationary Xi’s and Xi’s with a non-constant generalized variance function. Additionally, we analyze properties of multidimensional counterparts of the Pickands and Piterbarg constants that appear in the derived asymptotics. Important by-products of this contribution are the vector-process extensions of the Piterbarg inequality, the Borell–TIS inequality, the Slepian lemma and the Pickands–Piterbarg lemma which are the main pillars of the extremal theory of vector-valued Gaussian processes.

Keywords: Gaussian process; Conjunction; Extremes; Double-sum method; Slepian lemma; Borell–TIS inequality; Piterbarg inequality; Generalized Pickands constant; Generalized Piterbarg constant; Pickands–Piterbarg lemma (search for similar items in EconPapers)
Date: 2015
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (10)

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DOI: 10.1016/j.spa.2015.05.015

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