May 2024 A new shape of extremal clusters for certain stationary semi-exponential processes with moderate long range dependence
Zao-Li Chen, Gennady Samrodnitsky
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Bernoulli 30(2): 1105-1153 (May 2024). DOI: 10.3150/23-BEJ1626

Abstract

Extremal clusters of stationary processes with long memory can be quite intricate. For certain stationary infinitely divisible processes with subexponential tails an extremal cluster may consist of a single extreme value distributed over a stable regenerative set. This happens both in the case of power-like tails and in the case of certain lighter tails, e.g. lognormal-like tails, In this paper we show that in the case of semi-exponential tails, a new shape of extremal clusters arises. In this case each stable regenerative set supports a random panoply of varying extremes.

Funding Statement

This research was partially supported by the ARO grant W911NF-18-10318 and the NSF grant DMS-1506783 at Cornell University.

Acknowledgments

We are very grateful to the two anonymous referees and the AE who spent much time and effort on producing unusually detailed and helpful reports. The revised paper owes a lot to their suggestions.

Citation

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Zao-Li Chen. Gennady Samrodnitsky. "A new shape of extremal clusters for certain stationary semi-exponential processes with moderate long range dependence." Bernoulli 30 (2) 1105 - 1153, May 2024. https://doi.org/10.3150/23-BEJ1626

Information

Received: 1 July 2021; Published: May 2024
First available in Project Euclid: 31 January 2024

MathSciNet: MR4699547
Digital Object Identifier: 10.3150/23-BEJ1626

Keywords: Extreme value theory , Gumbel maximum domain of attraction , Long range dependence , random sup-measure , semi-exponential distributions , stable regenerative set , Subexponential distributions

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Vol.30 • No. 2 • May 2024
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