Extremal Value Theory for Long Range Dependent Stable Random Fields

2018/10/16 by Zaoli Chen, Chen, Zaoli, Gennady Samorodnitsky +1
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #60F17 #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Probability and Risk Models #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1810.07033

openalex publication_date 2018/10/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 cadlag 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.

Citations

• Limiting forms of the frequency distribution of the largest or smallest member of a sample

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