Canonical spectral representation for exchangeable max-stable sequences

The set L 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 of L is in one-to-one correspondence with the set F1 of distribution functions of non-negative random variables with unit mean. Consequently, each . L is uniquely represented by a pair (b, mu) of a constant b and a probability measure mu on F1. A canonical stochastic construction for arbitrary exchangeable max-stable sequences and a stochastic representation for the Pickands dependence measure of finite-dimensional margins of 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.