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2018 A family of random sup-measures with long-range dependence
Olivier Durieu, Yizao Wang
Electron. J. Probab. 23: 1-24 (2018). DOI: 10.1214/18-EJP235

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. "A family of random sup-measures with long-range dependence." Electron. J. Probab. 23 1 - 24, 2018. https://doi.org/10.1214/18-EJP235

Information

Received: 20 April 2018; Accepted: 10 October 2018; Published: 2018
First available in Project Euclid: 23 October 2018

zbMATH: 06970412
MathSciNet: MR3870450
Digital Object Identifier: 10.1214/18-EJP235

Subjects:
Primary: 60F17 , 60G70
Secondary: 60G57

Keywords: long-range dependence , point process convergence , random closed set , random sup-measure , regular variation , stationary process

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