On recurrence and transience of multivariate near-critical stochastic\n processes

2016/05/13 by Götz Kersting, Kersting, Götz
Mathematics · Physics and Astronomy · #60J10 #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.1605.04064

openalex publication_date 2016/05/13 · openalex created_date 2022/10/05 · openalex updated_date 2026/07/28

Abstract

We obtain complementary recurrence and transience criteria for processes\nX=(X_n)_{n \≥ 0} with values in mathbb R^d₊ fulfilling a non-linear\nequation X_n+1=MX_n+g(X_n)+ \ξ_n+1. Here M denotes a primitive matrix\nhaving Perron-Frobenius eigenvalue 1, and g denotes some function. The\nconditional expectation and variance of the noise (\ξ_n+1)_{n \≥ 0} are\nsuch that X obeys a weak form of the Markov property. The results generalize\ncriteria for the 1-dimensional case in [5].\n

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