Extremes of vector-valued Gaussian processes: Exact asymptotics

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Serveur académique Lausannois

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info:eu-repo/semantics/altIdentifier/doi/10.1016/j.spa.2015.05.015

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info:eu-repo/semantics/altIdentifier/pissn/0304-4149

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info:eu-repo/semantics/altIdentifier/urn/urn:nbn:ch:serval-BIB_90A8C2D02EF67

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Serveur Académique Lausannois

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Université de Lausanne et CHUV

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Gaussian process; Conjunction; Extremes; Double-sum method; Slepian lemma; Borell-TIS inequality; Piterbarg inequality; Generalized Pickands constant; Generalized Piterbarg constant; Pickands-Piterbarg lemma

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K. Dȩbicki et al., « Extremes of vector-valued Gaussian processes: Exact asymptotics », Serveur académique Lausannois, ID : 10.1016/j.spa.2015.05.015

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Let {X-i(t), t >= 0}, 1 infinity for both locally stationary X-i 's and X-i '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.

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