论文标题
随机混合系统的EM算法
EM algorithm for stochastic hybrid systems
论文作者
论文摘要
随机混合系统，也称为开关扩散，是一个连续的马尔可夫过程，其状态空间由离散和连续零件组成。我们考虑了离散状态转换的QMATRIX的参数估计以及扩散部分的漂移系数的参数估计。首先，我们在连续时间对样品路径的完全观察下得出了可能性函数。然后，扩展了Elliott等人开发的隐藏Markov模型的有限维过滤器。 （隐藏的马尔可夫模型，Springer，1995）至随机混合系统，我们在部分观察结果下得出了可能性函数和EM算法，在某种程度观察中，连续状态被及时地持续监测，而离散状态则未观察到。
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.
