Abstract
A stochastic hybrid system, also known as a switching diffusion, is a continuous-time Markov process with state space consisting of discrete and continuous parts. We consider parametric estimation of the Q matrix for the discrete state transitions and of the drift coefficient for the diffusion part. First, we derive the likelihood function under the complete observation of a sample path in continuous-time. Then, extending a finite-dimensional filter for hidden Markov models developed by Elliott et al. (Hidden Markov Models, Springer, 1995) to stochastic hybrid systems, we derive the likelihood function and the EM algorithm under a partial observation where the continuous state is monitored continuously in time, while the discrete state is unobserved.
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Fukasawa, M. EM algorithm for stochastic hybrid systems. Stat Inference Stoch Process 24, 223–239 (2021). https://doi.org/10.1007/s11203-020-09231-3
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DOI: https://doi.org/10.1007/s11203-020-09231-3