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Article Dans Une Revue Stochastic Processes and their Applications Année : 2009

Forgetting of the initial distribution for Hidden Markov Models

Résumé

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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Dates et versions

hal-00138902 , version 1 (28-03-2007)

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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, 2009, 119 (4), pp.1235--1256. ⟨hal-00138902⟩
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