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

Benoit Landelle, Eric Moulines, Elisabeth Gassiat

Publication date: 12 October 2008

Abstract: 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.

Mathematics Subject Classification ID

Filtering in stochastic control theory (93E11) Signal detection and filtering (aspects of stochastic processes) (60G35)

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