Probability and Statistics Seminar—— Identifying the infinitesimal generator of a stationary D-Markov chain using partially observable data
Holder： Xuyan Xiang ( Hunan University of Arts and Science)
Location：Room 1114, Sciences Building No. 1
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.
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