Forgetting of the initial distribution for non-ergodic Hidden Markov   Chains
  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. 
Elisabeth Gassiat (LM-Orsay), Benoit Landelle (LM-Orsay), Eric   Moulines (LTCI)