ρ^--混合序列自正则部分和之和乘积的几乎处处中心极限定理(英文)  

Almost Sure Central Limit Theorem for Self-normalized Products of Sums of Partial Sums of ρ^--mixing Sequences

作　　者：曹阳[1] 吴群英[1] 

机构地区：[1]桂林理工大学理学院,广西桂林541004

出　　处：《应用数学》2016年第2期438-450,共13页Mathematica Applicata

基　　金：Supported by the National Natural Science Fundation of China(11361019);the Program to Sponsor Teams for Innovation in the Construction of Talent Highlands in Guangxi Institutions of Higher Learning([2011]47);the Support Program of the Guangxi China Science Foundation(2013GXNSFDA019001);the Scientic Research Project of Guangxi Colleges and Universities(KY2015ZD054)

摘　　要：设X,X_1,X_2(,···是一严平稳的)ρ^--混合随机变量序列.在满足一定的条件下,证明自正则部分和之和乘积(k∏i=1T_4/i(i+1)μ/2)^(μ/βV_k)的几乎处处中心极限定理,其中Sn=∑_(i=1)~nX_i,V_n^2=∑_(i=1)~nX_i^2,Tn=∑_(i=1)~nSi.Let X,X_1,X_2,...be a strictly stationary sequence of ρ^--mixing random variables.A universal result in almost sure limit theorem for the self-normalized products of sum-（） μ∏kβVk∑s of partial sums （k∏i=1T_4/i（i＋1）μ/2）^（μ/βV_k） established,where Sn=∑_（i=1）~nX_i,V_n^2=∑_（i=1）~nX_i^2,Tn=∑_（i=1）~nSi.

关 键 词：ρ^--混合序列 自正则 部分和之和乘积 几乎处处中心极限定理 

分 类 号：O211.4[理学—概率论与数理统计]