Completely Operator Semi-Selfdecomposable Distributions
Completely Operator Semi-Selfdecomposable Distributions
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完全算子半自分解分布
DOI：
10.3836/tjm/1255958818
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发表时间：
2000
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
。研究了$R^{d}$上的完全算子半自可分解分布类$L_(b，q)$对$b$和$q$的性质。这里，$0<；b<；1$和$q$是一个$d\x d$矩阵，其特征值具有正实部。这是类$L_{m}(b，q)，$$m=-1，0，1，$的递减序列的极限类，其中$L_{-1}(b，q)$是$R^{d}$和$L_{m}(b，Q)$是L_{m-1}(b，q)$中满足$\hat{\mu}(z)=\hat{\mu}(b^{Q^{\prime}}z)\hat{\rho}(z)$的特征函数为$\fi$的分布族。$Q^$是$Q$的转置。利用高斯协方差矩阵和L测度刻画了$L(b，q)$中的分布。建立了与$R^{d}$上的算子半稳定分布类$OSS(b，q)$对于$b$和$q$的联系。
. The class $L_{\infty}(b, Q)$ of completely operator semi-selfdecomposable distributions on $R^{d}$ for $b$ and $Q$ is studied. Here $0<b<1$ and $Q$ is a $d\times d$ matrix whose eigenvalues have positive real parts. This is the limiting class of the decreasing sequence of classes $L_{m}(b, Q),$ $m=-1,0,1,$ $\cdots$ , where $L_{-1}(b, Q)$ is the class of all infinitely divisible distributions on $R^{d}$ and $L_{m}(b, Q)$ is defined inductively as the class of distributions $\mu$ with characteristic function $\hat{\mu}(z)$ satisfying $\hat{\mu}(z)=\hat{\mu}(b^{Q^{\prime}}z)\hat{\rho}(z)$ for some $\rho\in L_{m-1}(b, Q)$ . $Q^{\prime}$ is the transpose of $Q$ . Distributions in $L_{\infty}(b, Q)$ are characterized in terms of Gaussian covariance matrices and L \’evy measures. The connection with the class $OSS(b, Q)$ of operator semi-stable distributions on $R^{d}$ for $b$ and $Q$ is established.