We consider a reflection-type Markov chain which is usually used to characterize some process features in stochastic control and operations management. The existence of its stationary distributions is established by proving it to be the Feller chain, and its ergodicity is obtained by constructing the small set. Furthermore, for the non-ergodic case, the system dynamics are completely characterized.

中文翻译：

---

反射型马尔可夫链的平稳分布和遍历性

我们考虑一个反射型马尔可夫链，它通常用于表征随机控制和运营管理中的一些过程特征。通过证明它是Feller链来证明它的平稳分布的存在性，通过构造小集得到它的遍历性。此外，对于非遍历情况，系统动力学是完全表征的。