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Extremes of locally stationary Gaussian and chi fields on manifolds

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  • Qiao, Wanli

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.

Suggested Citation

  • Qiao, Wanli, 2021. "Extremes of locally stationary Gaussian and chi fields on manifolds," Stochastic Processes and their Applications, Elsevier, vol. 133(C), pages 166-192.
    • Handle: RePEc:eee:spapps:v:133:y:2021:i:c:p:166-192
    DOI: 10.1016/j.spa.2020.11.006
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