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.
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This research was partially supported by the NSF Grant DMS-1506783 and the ARO Grant W911NF-18-10318 at Cornell University.
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Chen, Z., Samorodnitsky, G. Extreme Value Theory for Long-Range-Dependent Stable Random Fields. J Theor Probab 33, 1894–1918 (2020). https://doi.org/10.1007/s10959-019-00951-8
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DOI: https://doi.org/10.1007/s10959-019-00951-8
Keywords
- Random field
- Extremal limit theorem
- Random sup measure
- Random closed set
- Long-range dependence
- Stable law
- Heavy tails