Operator Semi-Selfdecomposability, $(C,Q)$-Decomposability and Related Nested Classes
Operator Semi-Selfdecomposability, $(C,Q)$-Decomposability and Related Nested Classes
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运算符半自分解性、$(C,Q)$-可分解性和相关嵌套类
DOI：
10.3836/tjm/1270041450
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发表时间：
1999
影响因子：
0.6
通讯作者：
Toshiro Watanabe
中科院分区：
文献类型：
--
作者：
M. Maejima;Ken;Toshiro Watanabe
摘要关于$R^{d}，$ $d\geq 1$上概率测度的自可分解性有两种推广：Lo\'eve和Bunge的c-可分解性和C-可分解性，以及Maejima和Naito的半自可分解性.后者意味着无限可分性，但前者一般不意味着无限可分性。对于$d\geq 2$，引入算子（矩阵）正规化得到$R^{d}上的四类分布：L_{0}（B，Q），\tilde{L}_{0}（B，Q），$ $L_{0}（C，Q）$，$\tilde{L}_{0}（C，Q）$，其中0 <B<1，$ $Q$是特征值有正的真实的部分的$d\times d$矩阵，$C$是$[0，1]$中包含0 $和1的闭乘法子半群。此外，这些类中的每一个生成其子类的Urbanik-Sato型递减序列。这些类和子类的特征和关系的建立。它们补充和推广了Bunge，Jurek，Maejima和Naito，Sato和Yamazato的结果。
Summary. There are two types of generalizations of selfdecomposability of probability measures on $R^{d},$ $d\geq 1$ : the c-decomposability and the C-decomposability of Lo \‘eve and Bunge on the one hand, and the semi-selfdecomposability of Maejima and Naito on the other. The latter implies infinite divisibility but the former does not in general. For $d\geq 2$ introduction of operator (matrix) normalizations yields four kinds of classes of distributions on $R^{d}:L_{0}(b, Q),\tilde{L}_{0}(b, Q),$ $L_{0}(C, Q)$ , and $\tilde{L}_{0}(C, Q)$ , where $0<b<1,$ $Q$ is a $d\times d$ matrix with eigenvalues having positive real parts, and $C$ is a closed multiplicative subsemigroup of $[0,1]$ containing $0$ and 1. Further, each of these classes generates the Urbanik-Sato type decreasing sequence of its subclasses. Characterizations and relations of these classes and subclasses are established. They complement and generalize results of Bunge, Jurek, Maejima and Naito, and Sato and Yamazato.