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arXiv · 1809.05338

Canonical spectral representation for exchangeable max-stable sequences

Jan-Frederik Mai
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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.

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Jan-Frederik Mai. 2018-09-14. Canonical spectral representation for exchangeable max-stable sequences. https://doi.org/10.1007/s10687-019-00361-3

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