Non-(strong, geometrically) ergodicity criteria for discrete time Markov chains on general state
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866911339605131264 |
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| author | Wang, Ling-Di Chen, Yu Zhang, Yu-Hui |
| author_facet | Wang, Ling-Di Chen, Yu Zhang, Yu-Hui |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_18046 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Non-(strong, geometrically) ergodicity criteria for discrete time Markov chains on general state Wang, Ling-Di Chen, Yu Zhang, Yu-Hui Probability 60J05, 37B25 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. |
| title | Non-(strong, geometrically) ergodicity criteria for discrete time Markov chains on general state |
| topic | Probability 60J05, 37B25 |
| url | https://arxiv.org/abs/2503.18046 |