Study on a class of nonlinear time series models and ergodicity in random environment domain

In this paper, we study the problem of a variety of nonlinear threshold autoregressive model Xn+1=(Xn)+n+1(Zn+1) in which {Zn} is a Markov chain with finite state space, and for every state i of the Markov chain, {n(i)} is a sequence of independent and identically distributed random variables. Also, the limit behavior of the sequence {Xn} defined by the above model is investigated. Some new novel results on the underlying models are presented