Leírás
This presentation addresses nonlinear autoregressive models with exogenous regressors, which are essential tools in econometrics, queuing theory, and machine learning, yet whose statistical analysis is still incomplete. Established results, such as the law of large numbers and the functional central limit theorem, are available for weakly dependent variables. Here, we employ coupling arguments to demonstrate the transfer of mixing properties from the exogenous process to the response sequence.
Our study focuses on Markov chains in random environments (MCREs) with drift and minorization conditions, even with non-stationary environments exhibiting favorable mixing properties. Specifically, we establish both the law of large numbers and functional central limit theorems. As an application of this framework, we further investigate single-server queuing models, offering insights into their long-term behavior.