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On the maxima and sums of homogeneous Gaussian random fields

Author

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  • Tan, Zhongquan
  • Tang, Linjun

Abstract

Let {Xn}n≥1 be a sequence of homogeneous Gaussian random fields with mean 0 and variance 1. Under some conditions related to the correlation function of the field, the joint limiting distribution of the maximum and the sum of the Gaussian random field is obtained. The result is also extended to continuous time Gaussian random field.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:125:y:2017:i:c:p:44-54
    DOI: 10.1016/j.spl.2017.01.026
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    References listed on IDEAS

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    1. Tan, Zhongquan, 2013. "The limit theorems on extremes for Gaussian random fields," Statistics & Probability Letters, Elsevier, vol. 83(2), pages 436-444.
    2. 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.
    3. 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. Xiao, Jinghong & Wen, Yuechun & Tan, Zhongquan, 2019. "The limit properties of point processes of upcrossings in nonstationary strongly dependent Gaussian models," Statistics & Probability Letters, Elsevier, vol. 149(C), pages 38-46.
    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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