Extremes of Gaussian chaos processes with trend

Let X(t)=(X1(t),…,Xd(t)),t∈[0,S] be a Gaussian vector process and let g(x),x∈Rd be a continuous homogeneous function. We are concerned with the exact tail asymptotic of the chaos process g(X(t)),t∈[0,S] with a trend function h(t). Both scenarios X(t) is locally-stationary and X(t) is non-stationary...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2019-05, Vol.473 (2), p.1358-1376
Main Author: Bai, Long
Format: Article
Language:English
Subjects:
Asymptotic methods
Gaussian chaos
Gaussian vector processes
Pickands constant
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Summary:Let X(t)=(X1(t),…,Xd(t)),t∈[0,S] be a Gaussian vector process and let g(x),x∈Rd be a continuous homogeneous function. We are concerned with the exact tail asymptotic of the chaos process g(X(t)),t∈[0,S] with a trend function h(t). 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.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2019.01.026