EM algorithm for stochastic hybrid systems

A stochastic hybrid system, also known as a switching diffusion, is continuous-time Markov process with state space consisting of discrete and continuous parts. We consider parametric estimation the Q matrix for transitions drift coefficient diffusion part. First, we derive likelihood function under complete observation sample path in continuous-time. Then, extending finite-dimensional filter hidden models developed by Elliott et al. (Hidden Models, Springer, 1995) to systems, EM algorithm partial where monitored continuously time, while unobserved.