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The limit theorems on extremes for Gaussian random fields

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  • Tan, Zhongquan

Abstract

Motivated by the papers of Choi (2010) and Pereira (2010), in this work, we proved two limit theorems for the maxima of Gaussian fields. First, a Cox limit theorem is established for a stationary strongly dependent Gaussian random field. Second, a Gumbel type extreme limit theorem is proved for a non-stationary Gaussian random field with covariance functions satisfying the Cesàro convergence.

Suggested Citation

  • Tan, Zhongquan, 2013. "The limit theorems on extremes for Gaussian random fields," Statistics & Probability Letters, Elsevier, vol. 83(2), pages 436-444.
    • Handle: RePEc:eee:stapro:v:83:y:2013:i:2:p:436-444
    DOI: 10.1016/j.spl.2012.10.025
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    References listed on IDEAS

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    1. Ferreira, H. & Pereira, L., 2008. "How to compute the extremal index of stationary random fields," Statistics & Probability Letters, Elsevier, vol. 78(11), pages 1301-1304, August.
    2. Pereira, L., 2009. "The asymptotic location of the maximum of a stationary random field," Statistics & Probability Letters, Elsevier, vol. 79(20), pages 2166-2169, October.
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    Cited by:

    1. Tan, Zhongquan & Tang, Linjun, 2017. "On the maxima and sums of homogeneous Gaussian random fields," Statistics & Probability Letters, Elsevier, vol. 125(C), pages 44-54.
    2. Liu, Huiyan & Tan, Zhongquan, 2022. "Point processes of exceedances by Gaussian random fields with applications to asymptotic locations of extreme order statistics," Statistics & Probability Letters, Elsevier, vol. 189(C).

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