Forgetting of the initial distribution for non ergodic Hidden Markov Chains
Elisabeth Gassiat, Benoit Landelle and Eric Moulines
Annals of Applied Probability
In this paper, the forgetting of the initial distribution for non ergodic Hidden Markov Models 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 toital variation distance of the filter started from two intial different distributions and a convergence in expectation are considered. The results are illustrated using generic models of non ergodic HMMs.