A family of random sup-measures with long-range dependence

Olivier Durieu; Yizao Wang

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arXiv · 1804.07248

A family of random sup-measures with long-range dependence

Olivier Durieu·Yizao Wang

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Abstract

A family of self-similar and translation-invariant random sup-measures with long-range dependence are investigated. They are shown to arise as the limit of the empirical random sup-measure of a stationary heavy-tailed process, inspired by an infinite urn scheme, where same values are repeated at several random locations. The random sup-measure reflects the long-range dependence nature of the original process, and in particular characterizes how locations of extremes appear as long-range clusters represented by random closed sets. A limit theorem for the corresponding point-process convergence is established.

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Olivier Durieu, Yizao Wang. 2018-04-19. A family of random sup-measures with long-range dependence. https://arxiv.org/abs/1804.07248

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