A CENTRAL LIMIT THEOREM AND A STRONG MIXING CONDITION
A CENTRAL LIMIT THEOREM AND A STRONG MIXING CONDITION
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DOI：
10.1073/pnas.42.1.43
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发表时间：
1956-01-01
影响因子：
11.1
通讯作者：
ROSENBLATT, M
中科院分区：
文献类型：
--
作者：
ROSENBLATT, M
所需的假设是通常的二阶和2+ 6阶矩的假设和一个强混合条件。这个定理之所以有趣有两个原因。相依随机变量的所有一般中心极限定理在某种意义上都是由A.马尔可夫的效果，人们期望一个中心极限定理成立X1，X2，.，如果随机变量的行为更像独立随机变量，则它们分离得越远（假设存在适当的矩）。在S.伯恩斯坦关于中心极限定理的论文。本文中使用的强混合条件似乎是这个概念比大多数其他概念更直观的形式化。这个条件也很有趣，因为它是遍历理论中遇到的混合条件的一个强版本（见霍普夫，第2卷，第35页）。
The assumptions required are the usualassumptions on second and 2+ 6 order moments and a strong mixingcondition. The theorem is of interest for two reasons. All general central limit theorems for dependent random variables formalize in some sense a heuristic notion bf A. Markoff to the effect that one expects a central limit theorem to hold for Xi, X2,..., if the random variables behave more like independent randomvariables the farther they are separated (assuming that ap-propriate moments exist). An interesting discussion of this intuitive notion is given in S. Bernstein's paper on the central limit theorem.'The strong mixing condition used in this paper seems to be a more intuitively appealing formalization of this notion than most others. The condition is also of interest because it is a strong version of the mixing condition encountered in ergodic theory (see Hopf, 2 p. 35).