Unique Ergodicity of Non-Linear Filters via Reachability and Uniform Weak Continuity
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866912585070149632 |
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| author | Demirci, Yunus Emre Yüksel, Serdar |
| author_facet | Demirci, Yunus Emre Yüksel, Serdar |
| contents | We present a reachability based approach to establish unique ergodicity of non-linear filter processes where state space of a hidden Markov model is a compact Polish metric space and the observation space is a Polish metric space. We also establish a weak convergence result on occupation measures under such a reachability condition. Our conditions, which are explicit, are complementary to those based on filter stability as demonstrated in examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_15764 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Unique Ergodicity of Non-Linear Filters via Reachability and Uniform Weak Continuity Demirci, Yunus Emre Yüksel, Serdar Probability 60J05, 60J10, 93E11, 93E15 We present a reachability based approach to establish unique ergodicity of non-linear filter processes where state space of a hidden Markov model is a compact Polish metric space and the observation space is a Polish metric space. We also establish a weak convergence result on occupation measures under such a reachability condition. Our conditions, which are explicit, are complementary to those based on filter stability as demonstrated in examples. |
| title | Unique Ergodicity of Non-Linear Filters via Reachability and Uniform Weak Continuity |
| topic | Probability 60J05, 60J10, 93E11, 93E15 |
| url | https://arxiv.org/abs/2307.15764 |