Theory of Probability &Its Applications, Volume 65, Issue 4, Page 570-587, January 2021.
Let $X_t=\sum_{j=-\infty}^{\infty}A_j\varepsilon_{t-j}$ be a dependent linear process, where the $\{\varepsilon_n,\, n\in {Z}\}$ is a sequence of zero mean $m$-extended negatively dependent ($m$-END, for short) random variables which is stochastically dominated by a random variable $\varepsilon$, and $\{A_n,\, n\in {Z}\}$ is also a sequence of zero mean $m$-END random variables. Under some suitable conditions, the complete moment convergence for the dependent linear processes is established. In particular, the sufficient conditions of the complete moment convergence are provided. As an application, we further study the convergence of the state observers of linear-time-invariant systems.

中文翻译：

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用于线性时不变系统状态观测器的相依线性过程的完全矩收敛

Theory of Probability & Its Applications，第 65 卷，第 4 期，第 570-587 页，2021 年 1 月。
让 $X_t=\sum_{j=-\infty}^{\infty}A_j\varepsilon_{tj}$ 是一个相关的线性过程，其中 $\{\varepsilon_n,\, n\in {Z}\}$ 是零均值 $m$-扩展负相关（简称 $m$-END）随机变量的序列，随机变量由一个随机变量 $\varepsilon$，而 $\{A_n,\, n\in {Z}\}$ 也是一个零均值 $m$-END 随机变量的序列。在一些合适的条件下，建立了相关线性过程的完全矩收敛。特别是提供了完全矩收敛的充分条件。作为一个应用，我们进一步研究了线性时不变系统的状态观测器的收敛性。