Forward-reverse EM algorithm for Markov chains

We develop an EM algorithm for estimating parameters that determine the dynamics of a discrete time Markov chain evolving through a certain measurable state space. As a key tool for the construction of the EM method we also develop forward-reverse representations for Markov chains conditioned on a certain terminal state. These representations may be considered as an extension of the earlier work of Bayer and Schoenmakers (2013) on conditional diffusions. We present several experiments and consider the convergence of the new EM algorithm