Extremes of locally stationary Gaussian and chi fields on manifolds

Wanli Qiao

Stochastic Processes and their Applications, 2021, vol. 133, issue C, 166-192

Abstract: Depending on a parameter h∈(0,1], let {Xh(t),t∈Mh} be a class of centered Gaussian fields indexed by compact manifolds Mh with positive reach. For locally stationary Gaussian fields Xh, we study the asymptotic excursion probabilities of Xh on Mh. Two cases are considered: (i) h is fixed and (ii) h→0. These results are also extended to obtain the limit behaviors of the extremes of locally stationary χ-fields on manifolds.

Keywords: Local stationarity; Excursion probabilities; Gaussian fields; Chi-fields; Voronoi diagrams; Positive reach (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1016/j.spa.2020.11.006

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