Signal processing of semi-Markov models with exponentially decaying states

The authors straightforwardly modify hidden Markov model (HMM) processing, including the Baum-Welch reestimation formulae and related expectation maximization (EM) processing to deal with discrete-state, semi-Markov stochastic processes when their realizations are hidden (imbedded) in noise. They generalize such techniques to cope with exponential decay of states between step transitions. The motivation is that, in certain cases of biological signal processing, such models appear to be more appropriate than simpler ones. The time-varying transition probabilities of an underlying semi-Markov signal are unknown, `exponential´ decay rates between step transitions are unknown, and perhaps the noise statistics are not precisely known