Journal of Applied Mathematics and Stochastic Analysis
Volume 2005 (2005), Issue 3, Pages 345-351

Recursive smoothers for hidden discrete-time Markov chains

Lakhdar Aggoun

Department of Mathematics and Statistics, Sultan Qaboos University, P.O. Box 36, Al-Khodh, Muscat 123, Oman

Received 22 September 2004; Revised 4 February 2005

Copyright © 2005 Lakhdar Aggoun. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We consider a discrete-time Markov chain observed through another Markov chain. The proposed model extends models discussed by Elliott et al. (1995). We propose improved recursive formulae to update smoothed estimates of processes related to the model. These recursive estimates are used to update the parameter of the model via the expectation maximization (EM) algorithm.