On nonrecurrence of nonlinear random time delay autoregressive models under random environment

Abstract

In this paper, random environment and random time delay are introduced into general nonlinear autoregressive models to improve the applicability of these models. The introduction of random environment makes nonlinear autoregressive models more flexible and more widely used. Random time delay is a new way for models to be applied in new fields. In order to analyze the properties of the proposed new model, we construct a new stochastic process and prove that it is an irreducible and aperiodic time-homogeneous Markov chain. The nonrecurrence of the proposed new type of models is considered, and some sufficient conditions for nonrecurrence are investigated.

Keywords:

• Aperiodicity
• Irreducibility
• Markov process
• Nonrecurrence
• Random environment

MATHEMATICS SUBJECT CLASSIFICATION:

• 60J05
• 60J10
• 60K37

Acknowledgements

The authors would like to thank the Editor and anonymous referees for their valuable suggestions, which greatly improved our paper.

Additional information

Funding

This work was supported by the National Nature Science Foundation of China under Grant numbers 11461032 and 11401267, Jiangxi University of Science and Technology under the Program of Qingjiang Excellent Young Talents, and the Science Foundation of Jiangxi Provincial Education Department under Grant number GJJ190461.