Unique Ergodicity of Non-Linear Filters via Reachability and Uniform Weak Continuity
Probability
2025-09-16 v4
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.
Keywords
Cite
@article{arxiv.2307.15764,
title = {Unique Ergodicity of Non-Linear Filters via Reachability and Uniform Weak Continuity},
author = {Yunus Emre Demirci and Serdar Yüksel},
journal= {arXiv preprint arXiv:2307.15764},
year = {2025}
}