# Transition of α-mixing in Random Iterations with Applications in Queuing Theory

arXiv: https://arxiv.org/abs/2410.05056 · HTML: https://mlsanity.com/paper/2410.05056/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 55 references that are in the map.
- First posted on arXiv 7 Oct 2024.

## Builds on (most cited first, 5 of 5)

- [Optimization Methods for Large-Scale Machine Learning](https://mlsanity.com/paper/1606.04838/) (2016)
- [Markov chains in random environment with applications in queueing theory and machine learning](https://mlsanity.com/paper/1911.04377/) (2019)
- [Ergodic theorems for queuing systems with dependent inter-arrival times](https://mlsanity.com/paper/2004.01475/) (2020)
- [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)

## Abstract (arXiv)

Nonlinear time series models with exogenous regressors are essential in econometrics, queuing theory, and machine learning, though their statistical analysis remains incomplete. Key results, such as the law of large numbers and the functional central limit theorem, are known for weakly dependent variables. We demonstrate the transfer of mixing properties from the exogenous regressor to the response via coupling arguments. Additionally, we study Markov chains in random environments with drift and minorization conditions, even under non-stationary environments with favorable mixing properties, and apply this framework to single-server queuing models.