Open Access
August 2018 Extrema of rescaled locally stationary Gaussian fields on manifolds
Wanli Qiao, Wolfgang Polonik
Bernoulli 24(3): 1834-1859 (August 2018). DOI: 10.3150/16-BEJ913


Given a class of centered Gaussian random fields $\{X_{h}(s),s\in\mathbb{R}^{n},h\in(0,1]\}$, define the rescaled fields $\{Z_{h}(t)=X_{h}(h^{-1}t),t\in\mathcal{M}\}$, where $\mathcal{M}$ is a compact Riemannian manifold. Under the assumption that the fields $Z_{h}(t)$ satisfy a local stationary condition, we study the limit behavior of the extreme values of these rescaled Gaussian random fields, as $h$ tends to zero. Our main result can be considered as a generalization of a classical result of Bickel and Rosenblatt (Ann. Statist. 1 (1973) 1071–1095), and also of results by Mikhaleva and Piterbarg (Theory Probab. Appl. 41 (1997) 367–379).


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Wanli Qiao. Wolfgang Polonik. "Extrema of rescaled locally stationary Gaussian fields on manifolds." Bernoulli 24 (3) 1834 - 1859, August 2018.


Received: 1 August 2015; Revised: 1 October 2016; Published: August 2018
First available in Project Euclid: 2 February 2018

zbMATH: 06839253
MathSciNet: MR3757516
Digital Object Identifier: 10.3150/16-BEJ913

Keywords: Extreme values , local stationarity , triangulation of manifolds

Rights: Copyright © 2018 Bernoulli Society for Mathematical Statistics and Probability

Vol.24 • No. 3 • August 2018
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