Almost sure central limit theory for products of sums of partial sums  

作　　者：WU Qun-ying 

机构地区：[1]College of Science,Guilin University of Technology,Guilin 541004,China

出　　处：《Applied Mathematics(A Journal of Chinese Universities)》2012年第2期169-180,共12页高校应用数学学报（英文版）（B辑）

基　　金：Supported by the National Natural Science Foundation of China(11061012);Project Supported by Program to Sponsor Teams for Innovation in the Construction of Talent Highlands in Guangxi Institutions of Higher Learning([2011]47);the Guangxi Natural Science Foundation of China(2012GXNSFAA053010)

摘　　要：Consider a sequence of i.i.d.positive random variables.An universal result in almost sure limit theorem for products of sums of partial sums is established.We will show that the almost sure limit theorem holds under a fairly general condition on the weight dk= k-1 exp（lnβk）,0≤β〈1.And in a sense,our results have reached the optimal form.Consider a sequence of i.i.d.positive random variables.An universal result in almost sure limit theorem for products of sums of partial sums is established.We will show that the almost sure limit theorem holds under a fairly general condition on the weight dk= k-1 exp（lnβk）,0≤β〈1.And in a sense,our results have reached the optimal form.

关 键 词：almost sure central limit theorem WEIGHT product of sums of partial sums. 

分 类 号：O211.4[理学—概率论与数理统计] O211.5[理学—数学]