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

  • Zaoli Chen
  • Gennady SamorodnitskyEmail author
Article
  • 16 Downloads

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 

Mathematics Subject Classification (2010)

Primary 60G60 60G70 60G52 

Notes

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsCornell UniversityIthacaUSA
  2. 2.School of Operations Research and Information EngineeringCornell UniversityIthacaUSA

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