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Exponential forgetting and geometric ergodicity in hidden Markov models

François Le Gland 1 Laurent Mevel 1 
1 SIGMA2 - Signal, models, algorithms
IRISA - Institut de Recherche en Informatique et Systèmes Aléatoires, INRIA Rennes
Abstract : We consider a hidden Markov model with multidimensional observations, and with misspecification, i.e., the assumed coefficients (transition probability matrix and observation conditional densities) are possibly different from the true coefficients. Under mild assumptions on the coefficients of both the true and the assumed models, we prove that: (i) the prediction filter, and its gradient with respect to some parameter in the model, forget almost surely their initial condition exponentially fast, and (ii) the extended Markov chain, whose components are the unobserved Markov chain, the observation sequence, the prediction filter, and its gradient, is geometrically ergodic and has a unique invariant probability distribution.
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Submitted on : Sunday, December 1, 2013 - 11:34:40 PM
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François Le Gland, Laurent Mevel. Exponential forgetting and geometric ergodicity in hidden Markov models. Mathematics of Control, Signals, and Systems, Springer Verlag, 2000, 13 (1), pp.63-93. ⟨10.1007/PL00009861⟩. ⟨hal-00912073⟩



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