Filtering and change point estimation for hidden Markov-modulated Poisson processes

A continuous-time Markov chain which is partially observed in Poisson noise is considered, where a structural change in the dynamics of the hidden process occurs at a random change point. Filtering and change point estimation of the model is discussed. Closed-form recursive estimates of the conditional distribution of the hidden process and the random change point are obtained, given the Poisson process observations.