摘要
假设{X,Xn;n≥1}为平稳的负相伴随机变量序列.对其矩完全收敛的精确渐近性进行讨论.令EX1=0,E|X1|3<∞,且满足相应的条件.记Sn=X1+X2+…+Xn,n≥1,σ2=E X1+2∑∞j=2E(X1Xj)>0.若E|X|r<∞,1<p<2,r>1+p/2,成立li mε0ε2(2r--pp)-1∑∞n=1nr/p-2-1/pE{|Sn|-σεn1/p}+=(r-pp()(22-rp-)pσ-2)E|N|2(2r--pp),其中N为标准正态随机变量。
If (X,X,n≥1) is a stationary sequence of negatively associated random variables(NA), based on some means about convergence, precise asymptotics in the complete moment convergence of NA sequence is obtained. Suppose that EX1=0,E|X1|^3〈∞, some conditions are satisfied. Set Sn=X1+X2+4…Xn,n≥1, σ^2=EX1+2^∞∑j=2E( X1 Xj)〉0. If E|x|^r〈∞,1〈p〈2,r〉1+p/2, limx↘0 ε2(r-p)/2-p -1 ^∞∑n=1 m^r/p-2-1/p E{|Sn|-σεn^1/p}+=p(2-p)σ/(r-p)(2r-p-2)E|N|2(r-p)/2-p,where N is a standard normal random variable.
出处
《浙江大学学报(理学版)》
CAS
CSCD
北大核心
2005年第5期490-493,502,共5页
Journal of Zhejiang University(Science Edition)
基金
国家自然科学基金资助项目(10471126)
关键词
矩完全收敛性
负相伴随机变量
精确渐近性
moment convergence
negatively associated random variables
precise asymptotics