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Article Dans Une Revue The Annals of Applied Probability Année : 2010

Forgetting of the initial distribution for nonergodic Hidden Markov Chains

Résumé

In this paper, the forgetting of the initial distribution for a non-ergodic Hidden Markov Models (HMM) is studied. A new set of conditions is proposed to establish the forgetting property of the ¯lter, which signi¯cantly extends all the existing results. Both a pathwise and mean convergence of the total variation distance of the ¯lter started from two di®erent initial distributions are considered. The results are illustrated using a generic non-ergodic state-space models for which both pathwise and mean exponential stability is established
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hal-01354770 , version 1 (19-08-2016)

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  • HAL Id : hal-01354770 , version 1

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Randal Douc, Elisabeth Gassiat-Granier, Benoit Landelle, Éric Moulines. Forgetting of the initial distribution for nonergodic Hidden Markov Chains. The Annals of Applied Probability, 2010, 20 (5), pp.1638 - 1662. ⟨hal-01354770⟩
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