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

Zaoli Chen () and Gennady Samorodnitsky ()
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Zaoli Chen: Cornell University
Gennady Samorodnitsky: Cornell University

Journal of Theoretical Probability, 2020, vol. 33, issue 4, 1894-1918

Abstract: 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.

Keywords: Random field; Extremal limit theorem; Random sup measure; Random closed set; Long-range dependence; Stable law; Heavy tails; Primary 60G60; 60G70; 60G52 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s10959-019-00951-8

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