Open Access
August 2017 Tail asymptotics for the extremes of bivariate Gaussian random fields
Yuzhen Zhou, Yimin Xiao
Bernoulli 23(3): 1566-1598 (August 2017). DOI: 10.3150/15-BEJ788


Let $\{X(t)=(X_{1}(t),X_{2}(t))^{T},t\in\mathbb{R}^{N}\}$ be an $\mathbb{R}^{2}$-valued continuous locally stationary Gaussian random field with $\mathbb{E}[X(t)]=\mathbf{0}$. For any compact sets $A_{1},A_{2}\subset\mathbb{R}^{N}$, precise asymptotic behavior of the excursion probability \[\mathbb{P}(\max_{s\in A_{1}}X_{1}(s)>u,\max_{t\in A_{2}}X_{2}(t)>u)\qquad\mbox{as }u\rightarrow\infty\] is investigated by applying the double sum method. The explicit results depend not only on the smoothness parameters of the coordinate fields $X_{1}$ and $X_{2}$, but also on their maximum correlation $\rho$.


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Yuzhen Zhou. Yimin Xiao. "Tail asymptotics for the extremes of bivariate Gaussian random fields." Bernoulli 23 (3) 1566 - 1598, August 2017.


Received: 1 April 2015; Revised: 1 October 2015; Published: August 2017
First available in Project Euclid: 17 March 2017

zbMATH: 06714312
MathSciNet: MR3624871
Digital Object Identifier: 10.3150/15-BEJ788

Keywords: bivariate Gaussian field , bivariate Matérn field , double extremes , double sum method , excursion probability

Rights: Copyright © 2017 Bernoulli Society for Mathematical Statistics and Probability

Vol.23 • No. 3 • August 2017
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