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

• URL: http://arxiv.org/abs/2410.05056v2
• Date: Mon, 14 Oct 2024 08:53:16 GMT
• Title: Transition of $α$-mixing in Random Iterations with Applications in Queuing Theory
• Authors: Attila Lovas,
• Abstract summary: We show the transfer of mixing properties from the exogenous regressor to the response via coupling arguments. We also study Markov chains in random environments with drift and minorization conditions, even under non-stationary environments.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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