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

2008/10/12 by Elisabeth Gassiat, Gassiat, Elisabeth, Benoit Landelle +3
Mathematics · #60G35 #93E11 #FOS: Mathematics #Probability (math.PR) #math.PR #msc:60G35 #msc:93E11

paper · pdf · doi:10.48550/arxiv.0810.2123

31 pages

arxiv created 2008/10/12 · arxiv updated 2009/12/01

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.

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