Non-(strong, geometrically) ergodicity criteria for discrete time Markov chains on general state

Ling-Di Wang; Yu Chen; Yu-Hui Zhang

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arXiv · 2503.18046

Non-(strong, geometrically) ergodicity criteria for discrete time Markov chains on general state

Ling-Di Wang·Yu Chen·Yu-Hui Zhang

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Abstract

For discrete-time Markov chains on general state spaces, we establish criteria for non-ergodicity and non-strong ergodicity, and derive sufficient conditions for non-geometric ergodicity via the theory of minimal nonnegative solutions. Our criteria are formulated based on the existence of solutions to inequalities involving the chain's one-step transition kernel. Meanwhile, these practical criteria are applied to a type of examples, which can effectively characterize the non-ergodicity and non-strong ergodicity of a specific class of single birth (death) processes.

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Ling-Di Wang, Yu Chen, Yu-Hui Zhang. 2025-03-23. Non-(strong, geometrically) ergodicity criteria for discrete time Markov chains on general state. https://arxiv.org/abs/2503.18046

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