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 theQmatrix 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.

翻译：一个随机混合系统,又称切换扩散系统,是一个持续时间的马尔科夫过程,由离散和连续部件构成国家空间。我们考虑对离散状态转换和扩散部分漂移系数对Qmatrix的参数估计。首先,我们在连续时间对样本路径进行完整观察的基础上得出可能性功能。然后,将Elliott等人开发的隐藏的马尔科夫模型(Hidden Markov模型,Springer,1995年)的有限尺寸过滤器扩大到随机混合系统,我们在对连续状态进行持续监测的局部观察下得出可能性函数和EM算法,而离散状态则未观察到。