随机环境下AR型非线性时间序列的几何遍历性

摘要

Exponential autoregressive models, threshold autoregressive models and polynomial autoregressive models which are AR- type nonlinear time series models are widely used in engineering. But previous studies of AR- type nonlinear time series models, the interference is a single white noise sequence ,which can not reflect the factors of the interference in a system as well as the system itself influenced by sudden environment change. This article proposes a new type of AR- type nonlinear time series model under random environment, through the introduction of interference. The new model broadens the scope of application and enhances the adaptability of the model. Meanwhile, this article discussed the geometric ergodicity of the iterative sequence with the theory of stochastic stability on Markov chains and given a sufficient condition for convergence with geometric rate of the model .%指数自回归模型、门限自回归模型和多项式自回归模型等具有AR型非线性时间序列模型在工程中有广泛的应用.而以往研究的AR型非线性时间序列模型其干扰项为单一的白噪声序列,没有反映出动力系统受随机环境干扰的现象.文中引入随机环境的干扰,提出了随机环境下AR型非线性时间序列模型,拓宽了原模型的应用范围,增强了模型的适应性.同时利用马氏链的随机稳定性理论,研究了新模型的几何遍历性,给出了其以几何速率收敛的一个充分条件.