Under strong mixing on the Feynman-Kac model, particle filters and conditional particle filters forget their initial state in O(log N) steps, with an example showing optimality.
Under (A2), we obtain a lower bound for the densities of the ideal filters for large enough time indices, not depending on the initial distribution η0
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On the Forgetting of Particle Filters
Under strong mixing on the Feynman-Kac model, particle filters and conditional particle filters forget their initial state in O(log N) steps, with an example showing optimality.