A Unified Stability Theory for Classical and Monotone Markov Chains
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866929522448793600 |
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| author | Kamihigashi, Takashi Stachurski, John |
| author_facet | Kamihigashi, Takashi Stachurski, John |
| contents | This paper integrates two strands of the literature on stability of general state Markov chains: conventional, total variation based results and more recent order-theoretic results. First we introduce a complete metric over Borel probability measures based on partial stochastic dominance. We then show that many conventional results framed in the setting of total variation distance have natural generalizations to the partially ordered setting when this metric is adopted. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_00472 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Unified Stability Theory for Classical and Monotone Markov Chains Kamihigashi, Takashi Stachurski, John Probability This paper integrates two strands of the literature on stability of general state Markov chains: conventional, total variation based results and more recent order-theoretic results. First we introduce a complete metric over Borel probability measures based on partial stochastic dominance. We then show that many conventional results framed in the setting of total variation distance have natural generalizations to the partially ordered setting when this metric is adopted. |
| title | A Unified Stability Theory for Classical and Monotone Markov Chains |
| topic | Probability |
| url | https://arxiv.org/abs/2410.00472 |