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

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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Submitted on : Friday, October 12, 2018 - 1:02:06 PM
Last modification on : Tuesday, January 11, 2022 - 5:56:10 PM
Long-term archiving on: : Sunday, January 13, 2019 - 2:03:36 PM

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Olivier Durieu, Yizao Wang. A family of random sup-measures with long-range dependence. Electronic Journal of Probability, Institute of Mathematical Statistics (IMS), 2018, 23 (107), 24 pp. ⟨10.1214/18-EJP235⟩. ⟨hal-01771965v2⟩

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