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

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

2008-10-12

arxiv.org/abs/0810.2123v1

Mathematics

Probability

31 pages

Scientific paper

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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