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Extreme Value Theory for Long-Range-Dependent Stable Random Fields

Author

Listed:
  • Zaoli Chen

    (Cornell University)

  • Gennady Samorodnitsky

    (Cornell University)

Abstract

We study the extremes for a class of a symmetric stable random fields with long-range dependence. We prove functional extremal theorems both in the space of sup measures and in the space of càdlàg functions of several variables. The limits in both types of theorems are of a new kind, and only in a certain range of parameters, these limits have the Fréchet distribution.

Suggested Citation

  • Zaoli Chen & Gennady Samorodnitsky, 2020. "Extreme Value Theory for Long-Range-Dependent Stable Random Fields," Journal of Theoretical Probability, Springer, vol. 33(4), pages 1894-1918, December.
    • Handle: RePEc:spr:jotpro:v:33:y:2020:i:4:d:10.1007_s10959-019-00951-8
    DOI: 10.1007/s10959-019-00951-8
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    References listed on IDEAS

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    1. Takashi Owada, 2016. "Limit Theory for the Sample Autocovariance for Heavy-Tailed Stationary Infinitely Divisible Processes Generated by Conservative Flows," Journal of Theoretical Probability, Springer, vol. 29(1), pages 63-95, March.
    2. Arijit Chakrabarty & Parthanil Roy, 2013. "Group-Theoretic Dimension of Stationary Symmetric α-Stable Random Fields," Journal of Theoretical Probability, Springer, vol. 26(1), pages 240-258, March.
    3. Resnick, Sidney & Samorodnitsky, Gennady & Xue, Fang, 2000. "Growth rates of sample covariances of stationary symmetric [alpha]-stable processes associated with null recurrent Markov chains," Stochastic Processes and their Applications, Elsevier, vol. 85(2), pages 321-339, February.
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    Cited by:

    1. Rønn-Nielsen, Anders & Stehr, Mads, 2022. "Extremes of Lévy-driven spatial random fields with regularly varying Lévy measure," Stochastic Processes and their Applications, Elsevier, vol. 150(C), pages 19-49.

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