We show that the set of $d$-variate symmetric stable tail dependence functions, uniquely associated with exchangeable $d$-dimensional extreme-value copulas, is a simplex and determine its extremal boundary. The subset of elements which arises as $d$-margins of the set of $(d+k)$-variate symmetric stable tail dependence functions is shown to be proper for arbitrary $k \geq 1$. Finally, we derive an intuitive and useful necessary condition for a bivariate extreme-value copula to arise as bi-margin of an exchangeable extreme-value copula of arbitrarily large dimension, and thus to be conditionally iid.

中文翻译：

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可交换极值连接词的结构

我们表明，与可交换的 $d$ 维极值 copula 唯一相关的 $d$-variate 对称稳定尾依赖函数集是一个单纯形并确定其极值边界。作为 $(d+k)$-variate 对称稳定尾依赖函数集的 $d$-margins 出现的元素子集被证明适用于任意 $k \geq 1$。最后，我们推导出一个直观且有用的必要条件，使二元极值 copula 作为任意大维度的可交换极值 copula 的双边际出现，从而有条件地 iid。