Moderate deviations principle for products of sums of random variables  

作　　者：MIAO Yu MU JianYong 

机构地区：[1]College of Mathematics and Information Science,Henan Normal University,Xinxiang 453007,China

出　　处：《Science China Mathematics》2011年第4期769-784,共16页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China (Grant No.11001077)

摘　　要：Let(Xn)n≥1 be a sequence of independent identically distributed(i.i.d.) positive random variables with EX1 = μ,Var(X1) = σ2.In the present paper,we establish the moderate deviations principle for the products of partial sums(πnk=1Sk/n!μn)1/(γbn√(2n))1where γ = σ/μ denotes the coefficient of variation and(bn) is the moderate deviations scale.Let（Xn）n≥1 be a sequence of independent identically distributed（i.i.d.） positive random variables with EX1 = μ,Var（X1） = σ2.In the present paper,we establish the moderate deviations principle for the products of partial sums（Πnk=1Sk/n!μn）1/（γbn√（2n））1where γ = σ/μ denotes the coefficient of variation and（bn） is the moderate deviations scale.

关 键 词：moderate deviations principle products of sums independent identically distribution positive random variables 

分 类 号：O211.5[理学—概率论与数理统计] O212.6[理学—数学]