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- W4297922155 abstract "Let ${X_i(t),tge0}, 1le ile n$ be mutually independent centered Gaussian processes with almost surely continuous sample paths. We derive the exact asymptotics of $$ Pleft(exists_{t in [0,T]} forall_{i=1 ... n} X_i(t)> u right) $$ as $utoinfty$, 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." @default.
- W4297922155 created "2022-10-01" @default.
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- W4297922155 date "2015-05-24" @default.
- W4297922155 modified "2023-10-18" @default.
- W4297922155 title "Extremes of vector-valued Gaussian processes: exact asymptotics" @default.
- W4297922155 doi "https://doi.org/10.48550/arxiv.1505.06461" @default.
- W4297922155 hasPublicationYear "2015" @default.
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