Optimal stopping time on discounted semi-Markov processes  

作　　者：Fang CHEN Xianping GUO Zhong-Wei LIAO 

机构地区：[1]School of Mathematics,Sun Yat-Sen University,Guangzhou 510275,China [2]College of Education for the Future,Beijing Normal University,Beijing 100875,China

出　　处：《Frontiers of Mathematics in China》2021年第2期303-324,共22页中国高等学校学术文摘·数学（英文）

基　　金：This work was supported in part by the National Natural Science Foundation of China(Grant Nos.11931018,61773411,11701588,11961005);the Guangdong Basic and Applied Basic Research Foundation(Grant No.2020B1515310021).

摘　　要：This paper attempts to study the optimal stopping time for semi- Markov processes (SMPs) under the discount optimization criteria with unbounded cost rates. In our work, we introduce an explicit construction of the equivalent semi-Markov decision processes (SMDPs). The equivalence is embodied in the expected discounted cost functions of SMPs and SMDPs, that is, every stopping time of SMPs can induce a policy of SMDPs such that the value functions are equal, and vice versa. The existence of the optimal stopping time of SMPs is proved by this equivalence relation. Next, we give the optimality equation of the value function and develop an effective iterative algorithm for computing it. Moreover, we show that the optimal and ε-optimal stopping time can be characterized by the hitting time of the special sets. Finally, to illustrate the validity of our results, an example of a maintenance system is presented in the end.

关 键 词：Optimal stopping time semi-Markov processes(SMPs) value function semi-Markov decision processes(SMDPs) optimal policy iterative lgorithm 

分 类 号：O17[理学—数学]