揭示外生变量混杂性如何传递至响应变量，用于排队模型分析
Transition of $α$-mixing in Random Iterations with Applications in Queuing Theory
- 通过耦合论证建立外生变量混杂性向响应变量的传递机制
- 在非平稳环境中仍可保证马尔可夫链的收敛性与稳定性
- 为排队论中的单服务器模型提供理论支撑，适合统计与运筹研究者
包含外生回归变量的非线性时间序列模型在计量经济学、排队论和机器学习中至关重要，但其统计分析尚不完善。对于弱依赖变量，已知大数定律和函数中心极限定理。本文通过耦合论证，证明了外生回归变量的混杂性可传递至响应变量。此外，研究了具有漂移和小化条件的随机环境中的马尔可夫链，即使在非平稳环境下，只要具备良好的混杂性质，仍能成立。该框架被应用于单服务器排队模型。
原文摘要 · Abstract (English)
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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