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The limit theorems on extremes for Gaussian random fields

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  • Tan, Zhongquan
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    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.

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    File URL: http://www.sciencedirect.com/science/article/pii/S0167715212003975
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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 83 (2013)
    Issue (Month): 2 ()
    Pages: 436-444

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    Handle: RePEc:eee:stapro:v:83:y:2013:i:2:p:436-444

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    Related research

    Keywords: Cox limit theorem; Gumbel type extreme limit theorem; Extremes; Gaussian random fields; Strongly dependent;

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    1. 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.
    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.
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