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EM algorithm for stochastic hybrid systems

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  • Masaaki Fukasawa

    (Osaka University)

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.

Suggested Citation

  • Masaaki Fukasawa, 2021. "EM algorithm for stochastic hybrid systems," Statistical Inference for Stochastic Processes, Springer, vol. 24(1), pages 223-239, April.
    • Handle: RePEc:spr:sistpr:v:24:y:2021:i:1:d:10.1007_s11203-020-09231-3
    DOI: 10.1007/s11203-020-09231-3
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    References listed on IDEAS

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    1. Dembo, A. & Zeitouni, O., 1986. "Parameter estimation of partially observed continuous time stochastic processes via the EM algorithm," Stochastic Processes and their Applications, Elsevier, vol. 23(1), pages 91-113, October.
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