HAL: hal-00329515, version 1

arXiv: 0810.2123

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

Elisabeth Gassiat 1, Benoit Landelle 1, Eric Moulines 2

(2008-10-11)

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.

1:	Laboratoire de Mathématiques d'Orsay (LM-Orsay)
	CNRS : UMR8628 – Université Paris XI - Paris Sud
2:	Laboratoire Traitement et Communication de l'Information [Paris] (LTCI)
	Télécom ParisTech – CNRS : UMR5141

Subject

:

Mathematics/Probability Mathematics/Statistics

Keyword(s): Non-linear filtering – forgetting of the initial distribution – non-ergodic Hidden Markov Chains – Feynman-Kac semigroup

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From: Eric Moulines <>

Submitted on: Saturday, 11 October 2008 17:02:19

Updated on: Sunday, 12 October 2008 20:52:05