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Geometric Ergodicity in Hidden Markov Models

François Le Gland 1 Laurent Mevel 1, 2
1 SIGMA2 - Signal, models, algorithms
IRISA - Institut de Recherche en Informatique et Systèmes Aléatoires, INRIA Rennes
Abstract : We consider an 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 w.r.t. 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 : Wednesday, May 24, 2006 - 1:34:20 PM
Last modification on : Friday, May 20, 2022 - 9:04:45 AM
Long-term archiving on: : Sunday, April 4, 2010 - 11:55:38 PM


  • HAL Id : inria-00073706, version 1


François Le Gland, Laurent Mevel. Geometric Ergodicity in Hidden Markov Models. [Research Report] RR-2991, INRIA. 1996. ⟨inria-00073706⟩



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