论文标题
通过矩方法进行弱依赖的随机变量的中心极限定理
The Central Limit Theorem for Weakly Dependent Random Variables by the Moment Method
论文作者
论文摘要
在本文中，我们得出了一个中央限制定理，用于收集由离散度量空间索引的弱相关的随机变量，其中相关性衰减在索引的距离处。我们研究的相关结构仅取决于混合力矩的可分离性。我们的调查为CLT提供了新的证明，以$α$的混合随机变量，但也非$α$的随机变量适合我们的框架，例如MA（$ \ infty $）流程。特别是，我们的结果可以应用于具有独立白噪声的ARMA（$ P，Q $）过程。
In this paper, we derive a central limit theorem for collections of weakly correlated random variables indexed by discrete metric spaces, where the correlation decays in the distance of the indices. The correlation structure we study depends solely on the separability of mixed moments. Our investigation yields a new proof for the CLT for $α$-mixing random variables, but also non-$α$-mixing random variables fit within our framework, such as MA($\infty$) processes. In particular, our results can be applied to ARMA($p,q$) process with independent white noise.
