Given that most states in real systems are inaccessible, it becomes critical to study an inverse problem of an irreversibly stationary Markov chain how an infinitesimal generator can be identified using minimal observations. The hitting time distribution of an irreversibly stationary Markov chain is first determined by initially defining a stationary D-Markov chain. The hitting time distribution is then decoded via the taboo rate, and the results remarkably show that under mild conditions, the observations at all leaves and/or arbitrarily two-adjacent-states in each sub-cycle can be used to identify the infinitesimal generator. Several algorithms for accurately calculating the generator have also been proposed, and numerical examples are presented to confirm their efficiency and validity. It means that partially observable data can be used to identify the infinitesimal generator of a stationary D-Markov chain.

向绪言博士主要从事随机过程统计、计算及应用（生物信息、神经网络、随机计算与智能系统）方向的科研工作，发表论文40余篇。主持国家自然科学基金和省部级课题等10余项，参与国家自然科学基金等10多项。