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2018 Recurrence and transience of contractive autoregressive processes and related Markov chains
Martin P.W. Zerner
Electron. J. Probab. 23: 1-24 (2018). DOI: 10.1214/18-EJP152


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. "Recurrence and transience of contractive autoregressive processes and related Markov chains." Electron. J. Probab. 23 1 - 24, 2018.


Received: 31 December 2016; Accepted: 16 February 2018; Published: 2018
First available in Project Euclid: 15 March 2018

zbMATH: 1390.60263
MathSciNet: MR3779820
Digital Object Identifier: 10.1214/18-EJP152

Primary: 37H10 , 60J05 , 60J80

Keywords: autoregressive process , branching process , excited random walk , frog process , immigration , Lyapunov exponent , max-autoregressive process , Product of random matrices , random affine recursion , random difference equation , random environment , random exchange process , recurrence , super-heavy tail , transience


Vol.23 • 2018
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