论文标题
可交换的Min-ID序列：表征，指数测量和非负责ID-Processes
Exchangeable min-id sequences: Characterization, exponent measures and non-decreasing id-processes
论文作者
论文摘要
我们在（i）随机变量的可交换序列之间建立了一对一的对应关系，其有限维分布是最小（或最大）无限划分的，以及（ii）非负，无抵押的，无限的，无限分裂的随机过程。可交换最小除外序列的指数量度显示为非常简单的``漂移度量''的总和，并且是产品概率度量的混合物，该序列的混合物与非阴性和非抵押性无限划分的过程的Lévy度量唯一相对应。后者被证明是在非负和非负责函数上支持的。用概率术语，上述无限分开的过程等于与最小（或最大）无限分区边缘的随机变量可交换序列相关的条件累积危害过程。我们的结果提供了一个分析伞，该伞嵌入了许多有趣的多元分布类别的finetti亚家族，例如外源性冲击模型，指数和几何定量和缺乏内存性能，最小的多变量指数和极端价值分布，以及与完全单调的copul copul and Monotore-copul-copul copul and-trocimentiles copul-copul copul copul inotyentory Generorator，发电机。
We establish a one-to-one correspondence between (i) exchangeable sequences of random variables whose finite-dimensional distributions are minimum (or maximum) infinitely divisible and (ii) non-negative, non-decreasing, infinitely divisible stochastic processes. The exponent measure of an exchangeable minimum infinitely divisible sequence is shown to be the sum of a very simple ``drift measure'' and a mixture of product probability measures, which uniquely corresponds to the Lévy measure of a non-negative and non-decreasing infinitely divisible process. The latter is shown to be supported on non-negative and non-decreasing functions. In probabilistic terms, the aforementioned infinitely divisible process is equal to the conditional cumulative hazard process associated with the exchangeable sequence of random variables with minimum (or maximum) infinitely divisible marginals. Our results provide an analytic umbrella which embeds the de Finetti subfamilies of many interesting classes of multivariate distributions, such as exogenous shock models, exponential and geometric laws with lack-of-memory property, min-stable multivariate exponential and extreme-value distributions, as well as reciprocal Archimedean copulas with completely monotone generator and Archimedean copulas with log-completely monotone generator.
