负相伴随机变量序列矩完全收敛的精确渐近性

Precise asymptotics in the complete moment convergence of NA sequence.

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.