A General Law of Precise Asymptotics for Products of Sums under Dependence  

作　　者：Yong ZHANG Xiao Yun YANG Zhi Shan DONG 

机构地区：[1]College of Mathematics, Jilin University, Changchun 130012, P. R. China

出　　处：《Acta Mathematica Sinica,English Series》2010年第1期107-116,共10页数学学报（英文版）

基　　金：Supported by National Natural Science Foundation of China (Grant No. 10571073)

摘　　要：Let {Xn,n ≥ 1} be a strictly stationary LNQD （LPQD） sequence of positive random variables with EX1 = μ 〉 0, and VarX1 = σ^2 〈 ∞. Denote by Sn = ∑i=1^n Xi and γ = σ/μ the coefficients of variation. In this paper, under some suitable conditions, we show that a general law of precise asymptotics for products of sums holds. It can describe the relations among the boundary function, weighted function, convergence rate and limit value in the study of complete convergence.Let {Xn,n ≥ 1} be a strictly stationary LNQD （LPQD） sequence of positive random variables with EX1 = μ 〉 0, and VarX1 = σ^2 〈 ∞. Denote by Sn = ∑i=1^n Xi and γ = σ/μ the coefficients of variation. In this paper, under some suitable conditions, we show that a general law of precise asymptotics for products of sums holds. It can describe the relations among the boundary function, weighted function, convergence rate and limit value in the study of complete convergence.

关 键 词：general law precise asymptotics products of sums NA （PA） LNQD （LPQD） 

分 类 号：O151.21[理学—数学] O211.5[理学—基础数学]