Strong Stability of Linear Forms in φ-Mixing Random Variables  

作　　者：GAN Shixin 

机构地区：[1]School of Mathematics and Statistics, Wuhan University,Wuhan 430072, Hubei, China

出　　处：《Wuhan University Journal of Natural Sciences》2009年第1期6-10,共5页武汉大学学报（自然科学英文版）

基　　金：Supported by the National Natural Science Foundation of China(10671149)

摘　　要：In this paper some new results of strong stability of linear forms in φ-mixing random variables are given. It is mainly proved that for a sequence of φ-mixing random variables {xn,n≥1} and two sequences of positive numbers {an,n≥1} and {bn,n≥1} there exist d dn∈R,n = 1,2,..., such that bn^-1∑i=1^naixi-dn→0 a.s.under some suitable conditions. The results extend and improve the corresponding theorems for independent identically distributed random variables.In this paper some new results of strong stability of linear forms in φ-mixing random variables are given. It is mainly proved that for a sequence of φ-mixing random variables {xn,n≥1} and two sequences of positive numbers {an,n≥1} and {bn,n≥1} there exist d dn∈R,n = 1,2,..., such that bn^-1∑i=1^naixi-dn→0 a.s.under some suitable conditions. The results extend and improve the corresponding theorems for independent identically distributed random variables.

关 键 词：strong stability linear form φ-mixing random variable sequence strong law of large numbers 

分 类 号：O211.4[理学—概率论与数理统计] TN914.2[理学—数学]