Canonical spectral representation for exchangeable max-stable sequences
Abstract
The set of infinite-dimensional, symmetric stable tail dependence functions associated with exchangeable max-stable sequences of random variables with unit Fr\'echet margins is shown to be a simplex. Except for a single element, the extremal boundary is in one-to-one correspondence with the set of distribution functions of non-negative random variables with unit mean. Consequently, each element is uniquely represented by a pair of a constant and a probability measure on the space of distribution functions of non-negative random variables with unit mean. A canonical stochastic construction for arbitrary exchangeable max-stable sequences and a stochastic representation for the Pickands dependence measure of finite-dimensional margins are immediate corollaries. As by-products, a canonical analytical description and an associated canonical Le Page series representation for non-decreasing stochastic processes that are strongly infinitely divisible with respect to time are obtained.
Keywords
Cite
@article{arxiv.1809.05338,
title = {Canonical spectral representation for exchangeable max-stable sequences},
author = {Jan-Frederik Mai},
journal= {arXiv preprint arXiv:1809.05338},
year = {2020}
}