Electronic Journal of Probability

Recurrence and transience of contractive autoregressive processes and related Markov chains

Martin P.W. Zerner

Full-text: Open access

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.

Article information

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

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

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1521079340

Digital Object Identifier
doi:10.1214/18-EJP152

Mathematical Reviews number (MathSciNet)
MR3779820

Zentralblatt MATH identifier
1390.60263

Subjects
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]

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

Rights
Creative Commons Attribution 4.0 International License.

Citation

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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