High Extremes of Gaussian Chaos Processes: A Discrete Time Approximation Approach

Zhdanov, A. I.; Piterbarg, V. I.

doi:10.1137/s0040585x97t988885

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Cited by 7 publications

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“…The tail asymptotics of the supremum of Gaussian chaos processes has been recently derived in [1,2], see also [3] for a simpler case. Specifically, if X i 's are centered stationary and independent Gaussian processes with unit variance and common correlation function r satisfying r(t) = 1 − a|t| α + o(|t| α ), t → 0, a > 0, α ∈ (0, 2], r(t) < 1, t ∈ (0, T ], (1) then by [1] (under some restrictions on g)…”

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confidence: 99%

Extremes of Gaussian chaos processes with trend

Bai

2019

Journal of Mathematical Analysis and Applications

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Let X(t) = (X 1 (t), . . . , X d (t)), t ∈ [0, S] be a Gaussian vector process and let g(x), x ∈ R d be a continuous homogeneous function. In this paper we are concerned with the exact tail asymptotics of the chaos process g(X(t)) + h(t), t ∈ [0, S] with trend function h. Both scenarios X(t) is locally-stationary and X(t) is non-stationary are considered. Important examples include the product of Gaussian processes and chi-processes.

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