Abstract
In this paper, the forgetting of the initial distribution for a nonergodic Hidden Markov Models (HMM) is studied. A new set of conditions is proposed to establish the forgetting property of the filter. Both a pathwise and mean convergence of the total variation distance of the filter started from two different initial distributions are obtained. The results are illustrated using a generic nonergodic state-space model for which both pathwise and mean exponential stability is established.
Citation
Randal Douc. Elisabeth Gassiat. Benoit Landelle. Eric Moulines. "Forgetting of the initial distribution for nonergodic Hidden Markov Chains." Ann. Appl. Probab. 20 (5) 1638 - 1662, October 2010. https://doi.org/10.1214/09-AAP632
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