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

Zaoli Chen; Gennady Samorodnitsky

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arXiv · 2107.01517

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

Zaoli Chen·Gennady Samorodnitsky

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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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Zaoli Chen, Gennady Samorodnitsky. 2021-07-04. A New Shape of Extremal Clusters For Certain Stationary Semi-Exponential Processes With Moderate Long Range Dependence. https://arxiv.org/abs/2107.01517

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