## Electronic Communications in Probability

### On recurrence and transience of multivariate near-critical stochastic processes

Götz Kersting

#### 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
Accepted: 27 December 2016
First available in Project Euclid: 12 January 2017

https://projecteuclid.org/euclid.ecp/1484190065

Digital Object Identifier
doi:10.1214/16-ECP39

Zentralblatt MATH identifier
1357.60095

#### 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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