A family of random sup-measures with long-range dependence
Probability
2018-10-11 v2
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.
Keywords
Cite
@article{arxiv.1804.07248,
title = {A family of random sup-measures with long-range dependence},
author = {Olivier Durieu and Yizao Wang},
journal= {arXiv preprint arXiv:1804.07248},
year = {2018}
}
Comments
23 pages; minor revision