Convergence of Markov chain transition probabilities
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arXiv
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| Format: | Preprint |
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2020
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| _version_ | 1866908506578223104 |
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| author | Scheutzow, Michael Schindler, Juni |
| author_facet | Scheutzow, Michael Schindler, Juni |
| contents | Consider a discrete time Markov chain with rather general state space which has an invariant probability measure $μ$. There are several sufficient conditions in the literature which guarantee convergence of all or $μ$-almost all transition probabilities to $μ$ in the total variation (TV) metric: irreducibility plus aperiodicity, equivalence properties of transition probabilities, or coupling properties. In this work, we review and improve some of these criteria in such a way that they become necessary and sufficient for TV convergence of all respectively $μ$-almost all transition probabilities. In addition, we discuss so-called generalized couplings. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2004_10235 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Convergence of Markov chain transition probabilities Scheutzow, Michael Schindler, Juni Probability Primary 60J05, Secondary 60G10 Consider a discrete time Markov chain with rather general state space which has an invariant probability measure $μ$. There are several sufficient conditions in the literature which guarantee convergence of all or $μ$-almost all transition probabilities to $μ$ in the total variation (TV) metric: irreducibility plus aperiodicity, equivalence properties of transition probabilities, or coupling properties. In this work, we review and improve some of these criteria in such a way that they become necessary and sufficient for TV convergence of all respectively $μ$-almost all transition probabilities. In addition, we discuss so-called generalized couplings. |
| title | Convergence of Markov chain transition probabilities |
| topic | Probability Primary 60J05, Secondary 60G10 |
| url | https://arxiv.org/abs/2004.10235 |