Transition of $\alpha$-mixing in Random Iterations with Applications in Queuing Theory

TL;DR

This paper investigates how mixing properties transfer in nonlinear time series with exogenous regressors, establishing new results for Markov chains in random environments and applying them to queuing models.

Contribution

It introduces novel coupling techniques to transfer mixing properties and analyzes Markov chains in non-stationary environments with applications to queuing theory.

Findings

Transfer of mixing properties via coupling

Markov chains in non-stationary environments analyzed

Applications to single-server queuing models

Abstract

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.