WA17-1 10:00 Proc of the 36th IEEE CDC San Diego, CA Exponential Forgetting and Geometric Ergodicity in Hidden Markov Models*

We consider a hidden Markov model with multidimen-sional observations, and with misspecification, i.e. the assumed coefficients (transition probability matrix, and observation conditional densities) are possibly differ-ent 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 for-gets almost surely their initial condition exponentially fast, and (ii) the extended Markov chain, whose com-ponents are: the unobserved Markov chain, the obser-vation sequence, and the prediction filter, is geomet-rically ergodic, and has a unique invariant probability distribution.