Strict stationarity of AP(P) processes generated by nonlinear random functions with additive perturbations

Abstract

Let {X-n} be a generalized autoregressive process of order p defined by X-n = phi(n)(Xn-p,...,Xn-1) + eta(n), where {phi(n)} is a sequence of i.i.d. random maps taking values on H, and {eta(n)} is a Sequence of i.i.d. random variables. Let H be a collection of Borel measurable functions on R-p to R. By considering the associated Markov process, we obtain sufficient conditions for stationarity, (geometric) ergodicity of {X-n}.