New Classes of Infinitely Divisible Distributions Related to the Goldie-Steutel-Bondesson Class

几类无穷可分分布的嵌套子类的极限与稳定分布的闭包是一致的

The limits of nested subclasses of several classes of infinitely divisible distributions are identical with the closure of the class of stable distributions

证明了$R^d$上的五类无穷可分分布（Jurek类、Goldie-Steutel-Bondesson类、自分解分布类、Thorin类和广义型$G$分布类）的嵌套子类的极限与稳定分布类的闭包相同.还给出了更一般的结果。

Some new approaches to infinite divisibility

Using an approach based, amongst other things, on Proposition 1 of Kaluza (1928), Goldie (1967) and, using a different approach based especially on zeros of polynomials, Steutel (1967) have proved that each nondegenerate distribution function (d.f.) $F$ (on $\RR$, the real line), satisfying $F(0-) = 0$ and $F(x) = F(0) + (1-F(0)) G(x)$, $x > 0$, where $G$ is the d.f. corresponding to a mixture of exponential distributions, is infinitely divisible. Indeed, Proposition 1 of Kaluza (1928) implies that any nondegenerate discrete probability distribution ${p_x: x= 0,1, ...}$ that is log-convex or, …

对Bose-Dasgupta-Rubin（2002）《不可分割定律和过程综述》的补充

A Supplement To The Bose-Dasgupta-Rubin (2002) Review Of Infinitely Divisible Laws And Processes

本文证明了如果一个离散分布是具有整数值分量的无限可分分布（ID），那么它在原点有一个质量，这也意味着为什么某些ID离散律在其支撑中没有间隙。我们认为，离散的法律也可以是稳定的，这样的法律确实有吸引区域。然后给出了Bose Dasgupta Rubin（2002）在Sankhya的综述中没有报道的一些最新进展和参考文献，以及一些主题中的例子：离散律的无限可除性和稳定性，随机无限可除性，算子稳定律，L类律，Goldie-Steutel结果，极大无限可除性和稳定性，模拟，交替稳定律，应用和自由概率论。