A modified hidden Markov model

This paper considers two discrete time, finite state processes X and Y . In the usual hidden Markov model X modulates the values of Y . However, the values of Y are then i.i.d. given X . In this paper a new model is considered where the Markov chain X modulates the transition probabilities of the second, observed chain Y . This more realistically can represent problems arising in DNA sequencing. Algorithms for all related filters, smoothers and parameter estimations are derived. Versions of the Viterbi algorithms are obtained.