Electronic Journal of Probability

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

Olivier Durieu and Yizao Wang

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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.

Article information

Electron. J. Probab., Volume 23 (2018), paper no. 107, 24 pp.

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60G70: Extreme value theory; extremal processes 60F17: Functional limit theorems; invariance principles
Secondary: 60G57: Random measures

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

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Durieu, Olivier; Wang, Yizao. A family of random sup-measures with long-range dependence. Electron. J. Probab. 23 (2018), paper no. 107, 24 pp. doi:10.1214/18-EJP235. https://projecteuclid.org/euclid.ejp/1540260053

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