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The limit properties of point processes of upcrossings in nonstationary strongly dependent Gaussian models

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  • Xiao, Jinghong
  • Wen, Yuechun
  • Tan, Zhongquan

Abstract

Let {X(t),t≥0} be a nonstationary strongly dependent Gaussian process. Under some conditions related to the correlation function of the Gaussian process, the point processes formed by the upcrossings of level u by {X(t),t≥0} converge weakly to a Poisson process N with random intensity, as u→∞.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:149:y:2019:i:c:p:38-46
    DOI: 10.1016/j.spl.2019.01.028
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    References listed on IDEAS

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    1. Stamatovic, Biljana & Stamatovic, Sinisa, 2010. "Cox limit theorem for large excursions of a norm of a Gaussian vector process," Statistics & Probability Letters, Elsevier, vol. 80(19-20), pages 1479-1485, October.
    2. 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.
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    Cited by:

    1. 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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