We characterize recurrence and transience of nonnegative multivariate autoregressive processes of order one with random contractive coefficient matrix, of subcritical multitype Galton-Watson branching processes in random environment with immigration, and of the related max-autoregressive processes and general random exchange processes. Our criterion is given in terms of the maximal Lyapunov exponent of the coefficient matrix and the cumulative distribution function of the innovation/immigration component.
"Recurrence and transience of contractive autoregressive processes and related Markov chains." Electron. J. Probab. 23 1 - 24, 2018. https://doi.org/10.1214/18-EJP152