一类特殊随机二次型的极限定理  

Limit theorems of a special kind of random quadratic forms

作　　者：何宏儒[1] 

机构地区：[1]皖西学院数学系,安徽六安237012

出　　处：《合肥工业大学学报（自然科学版）》2005年第5期574-576,共3页Journal of Hefei University of Technology：Natural Science

摘　　要：文章采用鞅极限定理和一些矩阵不等式考查了一类特殊的随机二次形stAs的强、弱收敛性。当A为非负定矩阵且其最大特征根有限,随机变量存在有限的四阶矩情形下,获得了二次型的强收敛。并且该强收敛结果是一个传统极限定理的推广。当A为正定矩阵且其最大特征有限,在二阶矩有限的情况下,获得了二次型的弱收敛。In view of the need of practical application,strong and weak convergence of a special kind of random quadratic forms s^tAs are considered. When A is a nonnegative definite matrix with finite maximum eigenvalue, the strong convergence of random quadratic forms is established under finite fourth moment. This generalizes a classical limit theorem. When A is a positive definite matrix with finite maximum eigenvalue, convergence in probability is established as well. The limit theorems of martingale and some matrix inequalities are used in this paper.

关 键 词：强收敛 二次型 鞅差 非负定矩阵 

分 类 号：O211.4[理学—概率论与数理统计]