It has been well known for some time that for strictly stationary Markov chains that are ‘reversible’, the special symmetry (with the distribution of the Markov chain as a whole being invariant under a reversal of the ‘direction of time’) provides special extra features in the mathematical theory. This article here is in part an exposition of some of the basic aspects of that special theory. The mathematical techniques employed in this review are relatively gentle, involving only some basic measure-theoretic probability theory. To that special theory, a couple of new results are contributed here that are connected with the Rosenblatt strong mixing condition; and those new results in turn assist in bringing further clarity to the exposition of the theory.

中文翻译：

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严格平稳可逆马尔可夫链的一些基本特征

一段时间以来，众所周知，对于“可逆”的严格平稳马尔可夫链，特殊的对称性（马尔可夫链作为一个整体的分布在“时间方向”的反转下是不变的）提供了特殊的额外数学理论的特点。这篇文章部分地阐述了该特殊理论的一些基本方面。本综述中使用的数学技术相对温和，仅涉及一些基本的测度论概率论。对于这个特殊的理论，这里贡献了一些与 Rosenblatt 强混合条件相关的新结果；这些新结果反过来又有助于进一步阐明理论的阐述。