A New Shape of Extremal Clusters For Certain Stationary Semi-Exponential Processes With Moderate Long Range Dependence

2021/07/04 by Chen, Zaoli, Samorodnitsky, Gennady
#60F17 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2107.01517

Abstract

Extremal clusters of stationary processes with long memory can be quite intricate. For certain stationary infinitely divisible processes with subexponential tails, including both power-like tails and certain lighter tails, e.g. lognormal-like tails, such clusters may take the shape of stable regenerative sets. In this paper we show that for semi-exponential tails, which are even lighter, a new shape of extremal clusters arises. In this case each stable regenerative set supports a random panoply of varying extremes.

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