Recurrence and transience of contractive autoregressive processes and related Markov chains

Martin P. W. Zerner

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arXiv · 1608.01394

Recurrence and transience of contractive autoregressive processes and related Markov chains

Martin P. W. Zerner

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Abstract

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.

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Martin P. W. Zerner. 2016-08-03. Recurrence and transience of contractive autoregressive processes and related Markov chains. https://arxiv.org/abs/1608.01394

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