Canonical spectral representation for exchangeable max-stable sequences

09/14/2018

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by   Jan-Frederik Mai, et al.

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The set of infinite-dimensional, symmetric stable tail dependence functions associated with exchangeable max-stable sequences of random variables with unit Fréchet margins is shown to be a simplex. Except for an isolated point, the 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.