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
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
