We prove the existence of limiting distributions for a large class of Markov chains on a general state space in a random environment. We assume suitable versions of the standard drift and minorization conditions. In particular, the system dynamics should be contractive on the average with respect to the Lyapunov function and large enough small sets should exist with large enough minorization constants. We also establish that a law of large numbers holds for bounded functionals of the process. Applications to queuing systems, to machine learning algorithms and to autoregressive processes are presented.

中文翻译：

---

随机环境中的马尔可夫链及其在排队论和机器学习中的应用

我们证明了随机环境中一般状态空间上一大类马尔可夫链的极限分布的存在。我们假设标准漂移和最小化条件的合适版本。特别是，系统动力学应该相对于Lyapunov函数平均而言是收缩的，并且应该存在足够大的小集合，并且具有足够大的次要常数。我们还确定，该过程的有限功能适用大量定律。介绍了在排队系统，机器学习算法和自回归过程中的应用。