English

Recurrence and transience of contractive autoregressive processes and related Markov chains

Probability 2016-10-18 v2

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.

Keywords

Cite

@article{arxiv.1608.01394,
  title  = {Recurrence and transience of contractive autoregressive processes and related Markov chains},
  author = {Martin P. W. Zerner},
  journal= {arXiv preprint arXiv:1608.01394},
  year   = {2016}
}

Comments

Rewrote introduction, improved exposition, added references. Minor corrections. 26 pages