Central limit theorem for moving average processes generated by AANA random variable sequences
XU Huilian1, WANG Ying2
1.Career Foundation Department, Changchun Polytechnic, Changchun 130031, China 2.School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China
Abstract：Let {Xi,-∞<i<∞} be a sequence of identically distributed AANA random variables with EX1=0,0<EX12+δ<∞,limn→∞ESn2n=σ2>0,∑n=1∞qδ1+δ(n)<∞，for?some?0<δ<1. Let {ai,-∞<i<∞} be an absolutely summable sequence of real numbers with τ=∑i=-∞∞ai≠0. Denote Yn=∑i=-∞∞aiXn-i,Tn=∑j=1nYj,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.
徐惠莲, 王颖. 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[J]. 浙江大学学报（理学版）, 2021, 48(1): 64-68.
XU Huilian, WANG Ying. Central limit theorem for moving average processes generated by AANA random variable sequences. Journal of ZheJIang University(Science Edition), 2021, 48(1): 64-68.
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2021, Vol. 48 
