Unique Ergodicity of Non-Linear Filters via Reachability and Uniform Weak Continuity

Yunus Emre Demirci; Serdar Yüksel

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arXiv · 2307.15764

Unique Ergodicity of Non-Linear Filters via Reachability and Uniform Weak Continuity

Yunus Emre Demirci·Serdar Yüksel

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Abstract

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.

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Yunus Emre Demirci, Serdar Yüksel. 2023-07-28. Unique Ergodicity of Non-Linear Filters via Reachability and Uniform Weak Continuity. https://arxiv.org/abs/2307.15764

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