Electronic Communications in Probability

On recurrence and transience of multivariate near-critical stochastic processes

Götz Kersting

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Abstract

We obtain complementary recurrence/transience criteria for processes $X=(X_n)_{n \ge 0}$ with values in $\mathbb R^d_+$ fulfilling a non-linear equation $X_{n+1}=MX_n+g(X_n)+ \xi _{n+1}$. Here $M$ denotes a primitive matrix having Perron-Frobenius eigenvalue 1, and $g$ denotes some function. The conditional expectation and variance of the noise $(\xi _{n+1})_{n \ge 0}$ are such that $X$ obeys a weak form of the Markov property. The results generalize criteria for the 1-dimensional case in [5].

Article information

Source
Electron. Commun. Probab. Volume 22 (2017), paper no. 7, 12 pp.

Dates
Received: 17 May 2016
Accepted: 27 December 2016
First available in Project Euclid: 12 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1484190065

Digital Object Identifier
doi:10.1214/16-ECP39

Subjects
Primary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)

Keywords
Markov property recurrence transience Lyapunov function martingale

Rights
Creative Commons Attribution 4.0 International License.

Citation

Kersting, Götz. On recurrence and transience of multivariate near-critical stochastic processes. Electron. Commun. Probab. 22 (2017), paper no. 7, 12 pp. doi:10.1214/16-ECP39. https://projecteuclid.org/euclid.ecp/1484190065.


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References

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