Open Access
2017 On recurrence and transience of multivariate near-critical stochastic processes
Götz Kersting
Electron. Commun. Probab. 22: 1-12 (2017). DOI: 10.1214/16-ECP39


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].


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Götz Kersting. "On recurrence and transience of multivariate near-critical stochastic processes." Electron. Commun. Probab. 22 1 - 12, 2017.


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

zbMATH: 1357.60095
MathSciNet: MR3607802
Digital Object Identifier: 10.1214/16-ECP39

Primary: 60J10

Keywords: Lyapunov function , Markov property , martingale , recurrence , transience

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