NSD序列部分和乘积的渐近分布  

Asymptotic Distribution of Products of Partial Sums under NSD Sequences

作　　者：赵珈玉 陆冬梅 ZHAO Jiayu;LU Dongmei(College of Optical and Electronical Information,Changchun University of Science and Technology,Changchun 130114,China)

机构地区：[1]长春理工大学光电信息学院,长春130114

出　　处：《吉林大学学报（理学版）》2020年第6期1339-1344,共6页Journal of Jilin University:Science Edition

基　　金：吉林省自然科学基金(批准号:20170101061JC)。

摘　　要：设{X n,n≥1}是同分布正的负超可加相依(NSD)序列,利用NSD序列加权和的中心极限定理和大数定律,在适当的条件下证明当n→∞时,有{∏^nk=1 S^k/kμ)^1/(γσn)d→e^N,并讨论严平稳条件下的类似结论.其中:Sn=∑^ni=1Xi;μ=EX1>0;σ^2=Var X 1<∞;γ=σ/μ;σn^2=Var(1/γ∑^nk=1(Sk/kμ-1);N为标准正态随机变量.Let{X n,n≥1}be a sequence of identically distributed positive negatively superadditive dependent(NSD)random sequence.Under some suitable conditions,by using the central limit theorem of weighted sums and the law of large numbers of NSD random sequence,we prove that{∏^nk=1 S^k/kμ)^1/(γσn)d→e^N,n→∞.where Sn=∑^ni=1Xi;μ=EX1>0;σ^2=Var X 1<∞;γ=σ/μ;σn^2=Var(1/γ∑^nk=1(Sk/kμ-1);and N is a standard normal random variable,and we discuss similar conclusion for the strictly stationary case.

关 键 词：NSD序列 中心极限定理 同分布 对数正态分布 部分和乘积 

分 类 号：O211.4[理学—概率论与数理统计]