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Forgetting of the initial distribution for Hidden Markov Models

Abstract : The forgetting of the initial distribution for discrete Hidden Markov Models (HMM) is addressed: a new set of conditions is proposed, to establish the forgetting property of the filter, at a polynomial and geometric rate. 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 different HMM of interest: the dynamic tobit model, the non-linear state space model and the stochastic volatility model.
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https://hal.archives-ouvertes.fr/hal-00138902
Contributor : Gersende Fort <>
Submitted on : Wednesday, March 28, 2007 - 10:21:53 AM
Last modification on : Friday, July 31, 2020 - 10:44:06 AM
Long-term archiving on: : Wednesday, April 7, 2010 - 1:46:01 AM

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Randal Douc, Gersende Fort, Éric Moulines, Pierre Priouret. Forgetting of the initial distribution for Hidden Markov Models. Stochastic Processes and their Applications, Elsevier, 2009, 119 (4), pp.1235--1256. ⟨hal-00138902⟩

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