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