算子半稳定分布的分解  

Decomposition of operator semi-stable distribution.

作　　者：许鑫慧[1] 王成[1] 麻志浩[1] 

机构地区：[1]浙江大学数学系,浙江杭州310027

出　　处：《浙江大学学报（理学版）》2005年第3期256-257,263,共3页Journal of Zhejiang University（Science Edition）

基　　金：国家自然科学基金 (A0 3 2 5 10 3 )资助项目

摘　　要：JAJTE于1977年提出了算子半稳定分布的概念,并给出了满的算子半稳定分布μ的刻画:存在c(0 <c<1) ,h∈RN ,和RN上非奇异线性算子B,使得μc=Bμ* δ(h)成立.作者利用μ的对称群给出μc=Bμ* δ(h)的B,再利用B的最小多项式具体给出μ的分解,把μ分解为简单的Poisson部分和Gauss部分.The concept of operator semi-stable distributions on R N was introduced by Jajte, and an important fact was proved: a full distribution μ is operator semi-stable if and only if there exist a number c(0<c<1), a vector h∈R N, and a non-singular linear operator B in R N so that the formula μ c=Bμ*δ(h) holds. Here, the symmetric group of μ is used to characterize the operators B in μ c=Bμ*δ(h) and a decomposition of μ is given by the minimal polynomial of B so that μ=μ-1*μ-2, where μ-1 and μ-2 are Poissonian and Gaussian respectively.

关 键 词：算子半稳定 对称群 L-K表示 

分 类 号：O211.6[理学—概率论与数理统计]