Inverse Problems for Ergodicity of Markov Chains
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arXiv
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| Format: | Preprint |
| Published: |
2020
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| _version_ | 1866914781718380544 |
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| author | Wei, Zhi-Feng |
| author_facet | Wei, Zhi-Feng |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2001_00134 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Inverse Problems for Ergodicity of Markov Chains Wei, Zhi-Feng Probability 60J27, 60J10, 60J75, 82C22 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. |
| title | Inverse Problems for Ergodicity of Markov Chains |
| topic | Probability 60J27, 60J10, 60J75, 82C22 |
| url | https://arxiv.org/abs/2001.00134 |