The risk probability criterion for discounted continuous-time Markov decision processes
The risk probability criterion for discounted continuous-time Markov decision processes
复制标题
贴现连续时间马尔可夫决策过程的风险概率准则
DOI：
10.1007/s10626-017-0257-6
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发表时间：
2017-08
期刊：
影响因子：
--
通讯作者：
GuoXianping
中科院分区：
文献类型：
--
作者：
HuoHaifeng;ZouXiaolong;GuoXianping
In this paper, we consider the risk probability minimization problem for infinite discounted continuous-time Markov decision processes (CTMDPs) with unbounded transition rates. First, we introduce a class of policies depending on histories with the additional reward levels. Then, we construct the corresponding probability spaces, and also establish the non-explosion of the state process. Secondly, under suitable conditions we prove that the value function is a solution to the optimality equation for the probability criterion by an iteration technique, and obtain a value iteration algorithm to compute (at least approximate) the value function. Furthermore, under an additional condition we establish the uniqueness of the solution to the optimality equation and the existence of an optimal policy. Finally, we illustrate our results with two examples. The first one is used to verify our conditions for CTMDPs with unbounded transition rates, the second one for the numerical calculation of the value function and an optimal policy.
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DOI：
10.1017/s0021900200012882
发表时间：
2012-12
期刊：
J. Appl. Probab.
影响因子：
--
作者：
T. Prieto-Rumeau;O. Hernández-Lerma
通讯作者：
T. Prieto-Rumeau;O. Hernández-Lerma
DOI：
10.1007/978-3-319-04540-5_4
发表时间：
2015
期刊：
--
影响因子：
--
作者：
Philipp Melchiors
通讯作者：
Philipp Melchiors
DOI：
10.1016/s0022-247x(02)00097-5
发表时间：
2002-07
影响因子：
1.3
作者：
Yoshio Ohtsubo;K. Toyonaga
通讯作者：
Yoshio Ohtsubo;K. Toyonaga
DOI：
10.1007/s11768-013-2194-8
发表时间：
2013-10
期刊：
Journal of Control Theory and Applications
影响因子：
--
作者：
Masahiko Sakaguchi;Yoshio Ohtsubo
通讯作者：
Masahiko Sakaguchi;Yoshio Ohtsubo
DOI：
10.1007/0-387-70730-1
发表时间：
2007-03
期刊：
--
影响因子：
--
作者：
J. Janssen;R. Manca
通讯作者：
J. Janssen;R. Manca