Asymptotic properties of nonlinear autoregressive Markov processes with state-dependent switching

Authors:
Fubao Xi;G. Yin
Affiliations:
Department of Mathematics, Beijing Institute of Technology, Beijing 100081, People's Republic of China;Department of Mathematics, Wayne State University, Detroit, MI 48202, USA
Venue:
Journal of Multivariate Analysis
Year:
2010

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Abstract

In this paper, we consider a class of nonlinear autoregressive (AR) processes with state-dependent switching, which are two-component Markov processes. The state-dependent switching model is a nontrivial generalization of Markovian switching formulation and it includes the Markovian switching as a special case. We prove the Feller and strong Feller continuity by means of introducing auxiliary processes and making use of the Radon-Nikodym derivatives. Then, we investigate the geometric ergodicity by the Foster-Lyapunov inequality. Moreover, we establish the V-uniform ergodicity by means of introducing additional auxiliary processes and by virtue of constructing certain order-preserving couplings of the original as well as the auxiliary processes. In addition, illustrative examples are provided for demonstration.