复平稳随机序列均值遍历性的两个充要条件

Two Necessary and Sufficient Conditions of Mean Ergodicity about Compound Value Stationary Sequence

遍历性是平稳随机过程的一个核心问题,在实践中有重要的应用.这里首先给出复平稳序列均值遍历性的一个等价定义,在此基础上证明了复平稳序列情形下均值遍历性的两个充要条件,并给出一个形式简单的推论,这些结果有助于深入的理解复平稳过程的均值遍历性,同时也为估计复平稳过程的均值提供了一种简单高效的方法.

Ergodicity is a important property of stationary stochastic processes and has extensive application in practice, first we show an equivalent defination of the mean ergodicity to compound-value stationary sequence then the two sufficient and necessary conditions of mean ergodicity are proven and a widely used proposition is given in the end of article. The estimation of mean can be gotten affectivity.