Recursive algorithms for estimation of hidden Markov models and autoregressive models with Markov regime

This paper is concerned with recursive algorithms for the estimation of hidden Markov models (HMMs) and autoregressive (AR) models under the Markov regime. Convergence and rate of convergence results are derived. Acceleration of convergence by averaging of the iterates and the observations are treated. Finally, constant step-size tracking algorithms are presented and examined.