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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2502.13448 |
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| _version_ | 1866913737567371264 |
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| author | Li, Ting Liu, Xianming |
| author_facet | Li, Ting Liu, Xianming |
| contents | In this paper, we establish three criteria for the asymptotic behavior of Markov-Feller semigroups. First, we present a criterion for convergence in total variation to a unique invariant measure, requiring only $TV$-eventual continuity of the semigroup at a single point. Second, we propose two new criteria for asymptotic stability that require eventual continuity at a single point. This localized condition is more practical and easier to check. To illustrate the advantages of our framework, we provide an explicit example where verifying eventual continuity at a single point is straightforward, whereas establishing the corresponding global property is challenging. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_13448 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Criteria for asymptotic stability of eventually continuous Markov-Feller semigroups Li, Ting Liu, Xianming Probability In this paper, we establish three criteria for the asymptotic behavior of Markov-Feller semigroups. First, we present a criterion for convergence in total variation to a unique invariant measure, requiring only $TV$-eventual continuity of the semigroup at a single point. Second, we propose two new criteria for asymptotic stability that require eventual continuity at a single point. This localized condition is more practical and easier to check. To illustrate the advantages of our framework, we provide an explicit example where verifying eventual continuity at a single point is straightforward, whereas establishing the corresponding global property is challenging. |
| title | Criteria for asymptotic stability of eventually continuous Markov-Feller semigroups |
| topic | Probability |
| url | https://arxiv.org/abs/2502.13448 |