B值m相依随机元列移动平均过程的随机指标中心极限定理

The Central Limit Theorem for the Sum of Random Number of Moving Average Processes of m-Dependent B-Valued Elements

设{εt;t∈Z}是均值为零、二阶矩有限的B值m相依随机元列,{aj;j∈Z}是一实数序列,并且∑∞j=-∞aj<+∞.定义移动平均过程Xt=∑∞j=-∞ajεt-j(t≥1).利用Beveridge-Nelson分解及{εt;t≥1}的弱收敛定理,给出{Xt;t≥1}满足随机指标中心极限定理的充分条件.

Let{εt;t∈Z}be a sequence of m-dependent B-valued random elements with mean zeros and finite second moment.{αj;j∈Z}is a sequence of real numbers satisfying ∞∑jm｜αj｜〈＋∞. Define moving average process Xt=∞∑j=-∞ajεt-j（t≥1）,let Sn=n∑t=1Xt（n≥1）.Using Beveridge-Nelson decomposition and the weak convergence theorem of the sum of {εt;t≥1}we studied limit theorem of the sum of{Xt;t≥1} and gave a sufficient condition of the central limit theorem for the sum of random number of{Xt;t≥1} .