Forgetting of the initial distribution for non-ergodic Hidden Markov Chains

Elisabeth Gassiat (1) , Benoit Landelle (1) , Eric Moulines (2)

1 LM-Orsay - Laboratoire de Mathématiques d'Orsay
2 LTCI - Laboratoire Traitement et Communication de l'Information

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 filter, which significantly extends all the existing results. Both a pathwise-type convergence of the total variation distance of the filter started from two different initial distributions, and a convergence in expectation are considered. The results are illustrated using generic models of non-ergodic HMM and extend all the results known so far.

Mots clés: Non-linear filtering; forgetting of the initial distribution; non-ergodic Hidden Markov Chains; Feynman-Kac semigroup

Domaines: Probabilités [math.PR]; Statistiques [math.ST]

Elisabeth Gassiat, Benoit Landelle, Eric Moulines. Forgetting of the initial distribution for non-ergodic Hidden Markov Chains. 2008. ⟨hal-00329515⟩