On nonrecurrence of general nonlinear time series models with random time delay under random environment

This paper generalizes the general nonlinear time series model by introducing Markov chain with finite state space. On the one hand, we bring in random environment in the innovation process. On the other hand, we bring in random time delay which makes the order of the model turn to random rather than fixed. Nonrecurrence criteria for the Markov chain which is determined by the sequence of iterations of the new models are developed.