由渐近几乎负相协(AANA)随机变量序列生成的移动平均过程的中心极限定理

Central limit theorem for moving average processes generated by AANA random variable sequences

设{Xi,-∞<i<∞}为同分布的渐近几乎负相协(AANA)随机变量序列,当0<δ<1时,满足EX1=0,0<E|X1|^2+δ<∞,lim n→∞ESn^2/n=σ^2>0,∞Σn=1q^δ/1+δ(n)<∞。设{ai,-∞<i<∞}为绝对可和的实数序列,满足τ=∞Σi=-∞ai≠0。记Yn=∞Σi=-∞aiXn-i,Tn=nΣj=1Yj,n≥1,利用AANA随机变量序列的矩不等式和中心极限定理,在适当条件下,得到了由AANA随机变量序列生成的移动平均过程的中心极限定理,改进并推广了已有结果。

Let{Xi,-∞<i<∞}be a sequence of identically distributed AANA random variables with EX1=0,0<E|X1|^2+δ<∞,lim n→∞ESn^2/n=σ^2>0,∞Σn=1q^δ/1+δ(n)<∞,for some 0<δ<1.Let{ai,-∞<i<∞}be an absolutely summable sequence of real numbers withτ=Σi=-∞∞ai≠0.Denote Yn=∞Σi=-∞aiXn-i,Tn=nΣj=1Yj,n>1.Under some suitable conditions,using the moment inequality and central limit theorem of AANA random variable sequence,the central limit theorem for moving average processes generated by AANA random variable sequences is proved,which improves and extents the corresponding results.