ρ^--混合随机场的完全收敛性  

Complete convergence for ρ^--mixing random fields

作　　者：蔡光辉[1] 

机构地区：[1]浙江大学数学系,浙江杭州310028

出　　处：《浙江大学学报（理学版）》2003年第4期380-383,396,共5页Journal of Zhejiang University（Science Edition）

基　　金：国家自然科学基金(No.10071072)资助项目.

摘　　要：讨论了ρ--混合随机场的部分和完全收敛性.在一些适当的条件下,获得了较为一般的ρ--混合随机场的部分和完全收敛性定理,并得到了完全收敛速度与矩条件之间的等价关系.所得结果推广了ρ*-混合随机场和负相伴序列的相应结果.且将Hsu-Robbins型定理推广到ρ--混合随机场的情形.定理的证明基于Rosenthal型最大值不等式、Rosenthal型不等式、几个引理及缓变函数的性质.Complete convergence for sums of ρ- mixing random fields is discussed. More general theorems of complete convergence for sums of ρ- mixing random fields are obtained under some suitable conditions. And the equivalent relationship between rates of complete convergence and moment condition is obtained. The results obtained extend the relevant results for ρ*mixing random fields and negatively associated sequences. And HsuRobbins type theorem is generalized to the situation of ρ-mixing random fields. The proof is based on Rosenthal type maximal inequality, Rosenthal type inequality, several lemmas and properties of slowly varying function.

关 键 词：ρ^-—混合随机场 完全收敛性 完全收敛速度 矩条件 ρ^＊-混合随机场 负相伴序列 概率论 极限理论 

分 类 号：O211.4[理学—概率论与数理统计]