连续时间马尔可夫链的风险敏感控制

IF 0.8 4区数学 Q3 MATHEMATICS, APPLIED Stochastics-An International Journal of Probability and Stochastic Processes Pub Date : 2014-07-04 DOI:10.1080/17442508.2013.872644

M. K. Ghosh, Subhamay Saha

{"title":"连续时间马尔可夫链的风险敏感控制","authors":"M. K. Ghosh, Subhamay Saha","doi":"10.1080/17442508.2013.872644","DOIUrl":null,"url":null,"abstract":"We study risk-sensitive control of continuous time Markov chains taking values in discrete state space. We study both finite and infinite horizon problems. In the finite horizon problem we characterize the value function via Hamilton Jacobi Bellman equation and obtain an optimal Markov control. We do the same for infinite horizon discounted cost case. In the infinite horizon average cost case we establish the existence of an optimal stationary control under certain Lyapunov condition. We also develop a policy iteration algorithm for finding an optimal control.","PeriodicalId":49269,"journal":{"name":"Stochastics-An International Journal of Probability and Stochastic Processes","volume":"244 1","pages":"655 - 675"},"PeriodicalIF":0.8000,"publicationDate":"2014-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"56","resultStr":"{\"title\":\"Risk-sensitive control of continuous time Markov chains\",\"authors\":\"M. K. Ghosh, Subhamay Saha\",\"doi\":\"10.1080/17442508.2013.872644\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We study risk-sensitive control of continuous time Markov chains taking values in discrete state space. We study both finite and infinite horizon problems. In the finite horizon problem we characterize the value function via Hamilton Jacobi Bellman equation and obtain an optimal Markov control. We do the same for infinite horizon discounted cost case. In the infinite horizon average cost case we establish the existence of an optimal stationary control under certain Lyapunov condition. We also develop a policy iteration algorithm for finding an optimal control.\",\"PeriodicalId\":49269,\"journal\":{\"name\":\"Stochastics-An International Journal of Probability and Stochastic Processes\",\"volume\":\"244 1\",\"pages\":\"655 - 675\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2014-07-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"56\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Stochastics-An International Journal of Probability and Stochastic Processes\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1080/17442508.2013.872644\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Stochastics-An International Journal of Probability and Stochastic Processes","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1080/17442508.2013.872644","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 56

摘要

研究离散状态空间中连续时间马尔可夫链的风险敏感控制。我们研究有限和无限视界问题。在有限视界问题中，利用Hamilton Jacobi Bellman方程对值函数进行表征，得到了最优马尔可夫控制。我们对无限视界折现成本情况做同样的处理。在无限视界平均代价情况下，在一定的Lyapunov条件下，建立了最优平稳控制的存在性。我们还开发了一种策略迭代算法来寻找最优控制。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文

微信好友朋友圈 QQ好友复制链接

本刊更多论文

Risk-sensitive control of continuous time Markov chains

We study risk-sensitive control of continuous time Markov chains taking values in discrete state space. We study both finite and infinite horizon problems. In the finite horizon problem we characterize the value function via Hamilton Jacobi Bellman equation and obtain an optimal Markov control. We do the same for infinite horizon discounted cost case. In the infinite horizon average cost case we establish the existence of an optimal stationary control under certain Lyapunov condition. We also develop a policy iteration algorithm for finding an optimal control.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Stochastics-An International Journal of Probability and Stochastic Processes MATHEMATICS, APPLIED-STATISTICS & PROBABILITY

CiteScore

1.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Stochastics: An International Journal of Probability and Stochastic Processes is a world-leading journal publishing research concerned with stochastic processes and their applications in the modelling, analysis and optimization of stochastic systems, i.e. processes characterized both by temporal or spatial evolution and by the presence of random effects. Articles are published dealing with all aspects of stochastic systems analysis, characterization problems, stochastic modelling and identification, optimization, filtering and control and with related questions in the theory of stochastic processes. The journal also solicits papers dealing with significant applications of stochastic process theory to problems in engineering systems, the physical and life sciences, economics and other areas. Proposals for special issues in cutting-edge areas are welcome and should be directed to the Editor-in-Chief who will review accordingly. In recent years there has been a growing interaction between current research in probability theory and problems in stochastic systems. The objective of Stochastics is to encourage this trend, promoting an awareness of the latest theoretical developments on the one hand and of mathematical problems arising in applications on the other.