Inverse Problems for Ergodicity of Markov Chains

Zhi-Feng Wei

doi:10.1016/j.jmaa.2021.125483

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arXiv · 2001.00134

Inverse Problems for Ergodicity of Markov Chains

Zhi-Feng Wei

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Abstract

For both continuous-time and discrete-time Markov Chains, we provide criteria for inverse problems of classical types of ergodicity: (ordinary) erogodicity, algebraic ergodicity, exponential ergodicity and strong ergodicity. Our criteria are in terms of the existence of solutions to inequalities involving the $Q$-matrix (or transition matrix $P$ in time-discrete case) of the process. Meanwhile, these criteria are applied to some examples and provide "universal" treatment, including single birth processes and several multi-dimensional models.

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Zhi-Feng Wei. 2020-01-01. Inverse Problems for Ergodicity of Markov Chains. https://doi.org/10.1016/j.jmaa.2021.125483

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