The set \(\mathfrak {L}\) 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 a single element, the extremal boundary of \(\mathfrak {L}\) is in one-to-one correspondence with the set \(\mathfrak {F}_{1}\) of distribution functions of non-negative random variables with unit mean. Consequently, each \(\ell \in \mathfrak {L}\) is uniquely represented by a pair (b, µ) of a constant b and a probability measure µ on \(\mathfrak {F}_{1}\). A canonical stochastic construction for arbitrary exchangeable max-stable sequences and a stochastic representation for the Pickands dependence measure of finite-dimensional margins of l 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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可交换的最大稳定序列的规范光谱表示

无限维，对称稳定尾部依赖函数的集合\（\ mathfrak {L} \）与具有单位Fréchet边距的随机变量的可交换最大稳定序列相关联，显示为单形。除单个元素外，\（\ mathfrak {L} \）的极值边界与非负分布函数的集合\（\ mathfrak {F} _ {1} \）一一对应具有单位均值的随机变量。因此，每个\（\ ell \ in \ mathfrak {L} \）由一对（b，µ）的常数b和\（\ mathfrak {F} _ {1} \）上的概率度量µ唯一表示。。任意可交换的最大稳定序列的规范随机构造和l的有限维边距的Pickands依赖度量的随机表示是直接推论。作为副产品，获得了关于非递减随机过程的规范分析说明和相关的规范Le Page系列表示，该随机过程相对于时间可以无限地整除。