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Extremes of Gaussian fields with a smooth random variance

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  • Popivoda, Goran
  • Stamatović, Siniša

Abstract

In this paper we investigate the probabilities of large extremes P(supt∈Tξ(t)η(t)>u), as u→∞, where ξ(t) is a centered homogeneous Gaussian random field, η(t) is particular smooth field independent of ξ(t) and T⊂Rn is a closed Jordan set.

Suggested Citation

  • Popivoda, Goran & Stamatović, Siniša, 2016. "Extremes of Gaussian fields with a smooth random variance," Statistics & Probability Letters, Elsevier, vol. 110(C), pages 185-190.
    • Handle: RePEc:eee:stapro:v:110:y:2016:i:c:p:185-190
    DOI: 10.1016/j.spl.2015.12.022
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    References listed on IDEAS

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    1. Arendarczyk, Marek & Dȩbicki, Krzysztof, 2012. "Exact asymptotics of supremum of a stationary Gaussian process over a random interval," Statistics & Probability Letters, Elsevier, vol. 82(3), pages 645-652.
    2. Hösler, Jörg & Piterbarg, Vladimir & Rumyantseva, Ekaterina, 2011. "Extremes of Gaussian processes with a smooth random variance," Stochastic Processes and their Applications, Elsevier, vol. 121(11), pages 2592-2605, November.
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    Cited by:

    1. Pingjin Deng, 2018. "The Joint Distribution of Running Maximum of a Slepian Process," Methodology and Computing in Applied Probability, Springer, vol. 20(4), pages 1123-1135, December.

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