m-相依随机变量序列的中心极限定理及逼近速度

The central limit theorem and the approximation rate of m-dependent random variables

令m-相依的随机变量{Xk,k≥1}是一同分布且平稳的序列,且存在随机数列{Nn,n≥1}与序列{Xk,k≥1}独立,关于该序列的部分和为SNn=∑Nnj=1Xj.则在Nn的某些假设条件下可得到随机变量Xk的部分和序列{SNn,n≥1}的极限分布,以及其与标准正态分布逼近速度的估计.

Let the m-dependent random variables{Xk,k≥1}be a stationary sequence with a common distribution,and there is a random number{Nn,n≥1},independent of the sequence{Xk,k≥1},SNn=∑Nnj=1Xj express the partial sums of sequence{Xk,k≥1}.So under some conditions for the random number Nn,we can get the results on limit distribution of the sequence{SNn,n≥1},and an estimate of the rate of approximation after suitable normalization.