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Conference Papers Year : 1997

Exponential forgetting and geometric ergodicity in HMM's

François Le Gland
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Laurent Mevel


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: 1) the prediction filter forgets almost surely their initial condition exponentially fast; and 2) the extended Markov chain, whose components are the unobserved Markov chain, the observation sequence and the prediction filter, is geometrically ergodic, and has a unique invariant probability distribution.
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hal-00912076 , version 1 (20-12-2013)



François Le Gland, Laurent Mevel. Exponential forgetting and geometric ergodicity in HMM's. Proceedings of the 36th Conference on Decision and Control, San Diego 1997, IEEE--CSS, Dec 1997, San Diego, United States. pp.537-542, ⟨10.1109/CDC.1997.650683⟩. ⟨hal-00912076⟩
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