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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Stochastic Processes and their Applications, Elsevier, 2009, 119 (4), pp.1235--1256
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Dernière modification le : jeudi 27 avril 2017 - 09:46:38
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Randal Douc, Gersende Fort, Eric 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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