# Markov chains in random environment with applications in queueing theory and machine learning

arXiv: https://arxiv.org/abs/1911.04377 · HTML: https://mlsanity.com/paper/1911.04377/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Nov 2019.

## Built on by (most cited first, 3 of 3)

- [Functional Central Limit Theorem and Strong Law of Large Numbers for Stochastic Gradient Langevin Dynamics](https://mlsanity.com/paper/2210.02092/) (2022)
- [On the strong stability of ergodic iterations](https://mlsanity.com/paper/2304.04657/) (2023)
- [Transition of α-mixing in Random Iterations with Applications in Queuing Theory](https://mlsanity.com/paper/2410.05056/) (2024)

## Abstract (arXiv)

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.