Electronic Journal of Probability

Recurrence and transience of contractive autoregressive processes and related Markov chains

Martin P.W. Zerner

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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.

Article information

Electron. J. Probab., Volume 23 (2018), paper no. 27, 24 pp.

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

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Zentralblatt MATH identifier

Primary: 60J05: Discrete-time Markov processes on general state spaces 60J80: Branching processes (Galton-Watson, birth-and-death, etc.) 37H10: Generation, random and stochastic difference and differential equations [See also 34F05, 34K50, 60H10, 60H15]

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

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Zerner, Martin P.W. Recurrence and transience of contractive autoregressive processes and related Markov chains. Electron. J. Probab. 23 (2018), paper no. 27, 24 pp. doi:10.1214/18-EJP152. https://projecteuclid.org/euclid.ejp/1521079340

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