Extremes of Gaussian chaos processes with trend

Long Bai

doi:10.1016/j.jmaa.2019.01.026

Extremes of Gaussian chaos processes with trend

Long Bai^*

^*Corresponding author for this work

Department of Financial and Actuarial Mathematics

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

Let X(t)=(X₁(t),…,X_d(t)),t∈[0,S] be a Gaussian vector process and let g(x),x∈R^d 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.

Original language	English
Pages (from-to)	1358-1376
Number of pages	19
Journal	Journal of Mathematical Analysis and Applications
Volume	473
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2019.01.026
Publication status	Published - 15 May 2019

Keywords

Asymptotic methods
Gaussian chaos
Gaussian vector processes
Pickands constant

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10.1016/j.jmaa.2019.01.026

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AB - 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.

KW - Asymptotic methods

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KW - Gaussian vector processes

KW - Pickands constant

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ER -

Extremes of Gaussian chaos processes with trend

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