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Regularly varying random fields

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  • Wu, Lifan
  • Samorodnitsky, Gennady

Abstract

We study the extremes of multivariate regularly varying random fields. The crucial tools in our study are the tail field and the spectral field, notions that extend the tail and spectral processes of Basrak and Segers (2009). The spatial context requires multiple notions of extremal index, and the tail and spectral fields are applied to clarify these notions and other aspects of extremal clusters. An important application of the techniques we develop is to the Brown–Resnick random fields.

Suggested Citation

  • Wu, Lifan & Samorodnitsky, Gennady, 2020. "Regularly varying random fields," Stochastic Processes and their Applications, Elsevier, vol. 130(7), pages 4470-4492.
    • Handle: RePEc:eee:spapps:v:130:y:2020:i:7:p:4470-4492
    DOI: 10.1016/j.spa.2020.01.005
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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. Einmahl, J.H.J. & de Haan, L.F.M. & Li, D., 2006. "Weighted approximations of tail copula processes with applications to testing the bivariate extreme value condition," Other publications TiSEM 18b65ac3-ba79-4bff-ad53-2, Tilburg University, School of Economics and Management.
    3. Basrak, Bojan & Segers, Johan, 2009. "Regularly varying multivariate time series," Stochastic Processes and their Applications, Elsevier, vol. 119(4), pages 1055-1080, April.
    4. Schlather, Martin, 2001. "Examples for the coefficient of tail dependence and the domain of attraction of a bivariate extreme value distribution," Statistics & Probability Letters, Elsevier, vol. 53(3), pages 325-329, June.
    5. Davis, Richard A. & Mikosch, Thomas, 2008. "Extreme value theory for space-time processes with heavy-tailed distributions," Stochastic Processes and their Applications, Elsevier, vol. 118(4), pages 560-584, April.
    6. Hult, Henrik & Lindskog, Filip, 2005. "Extremal behavior of regularly varying stochastic processes," Stochastic Processes and their Applications, Elsevier, vol. 115(2), pages 249-274, February.
    7. Lien, Da-Hsiang Donald, 1986. "Moments of ordered bivariate log-normal distributions," Economics Letters, Elsevier, vol. 20(1), pages 45-47.
    8. Yong Bum Cho & Richard A. Davis & Souvik Ghosh, 2016. "Asymptotic Properties of the Empirical Spatial Extremogram," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(3), pages 757-773, September.
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    Cited by:

    1. Damek, Ewa & Mikosch, Thomas & Zhao, Yuwei & Zienkiewicz, Jacek, 2023. "Whittle estimation based on the extremal spectral density of a heavy-tailed random field," Stochastic Processes and their Applications, Elsevier, vol. 155(C), pages 232-267.
    2. Hashorva, Enkelejd & Kume, Alfred, 2021. "Multivariate max-stable processes and homogeneous functionals," Statistics & Probability Letters, Elsevier, vol. 173(C).

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