We study a class of discounted models of singular stochastic control. In thiskind of models, not only the structure of cost function has been extended to some general type, butalso the state can be represented as the ...We study a class of discounted models of singular stochastic control. In thiskind of models, not only the structure of cost function has been extended to some general type, butalso the state can be represented as the solution of a class of stochastic differential equationswith nonlinear drift and diffusion term. By the various methods of stochastic analysis, we derivethe sufficient and necessary conditions of the existence of optimal control.展开更多
This paper studies the strong n(n =—1,0)-discount and finite horizon criteria for continuoustime Markov decision processes in Polish spaces.The corresponding transition rates are allowed to be unbounded,and the rewar...This paper studies the strong n(n =—1,0)-discount and finite horizon criteria for continuoustime Markov decision processes in Polish spaces.The corresponding transition rates are allowed to be unbounded,and the reward rates may have neither upper nor lower bounds.Under mild conditions,the authors prove the existence of strong n(n =—1,0)-discount optimal stationary policies by developing two equivalence relations:One is between the standard expected average reward and strong—1-discount optimality,and the other is between the bias and strong 0-discount optimality.The authors also prove the existence of an optimal policy for a finite horizon control problem by developing an interesting characterization of a canonical triplet.展开更多
基金This research is supported by the National Natural Science Foundation of China
文摘We study a class of discounted models of singular stochastic control. In thiskind of models, not only the structure of cost function has been extended to some general type, butalso the state can be represented as the solution of a class of stochastic differential equationswith nonlinear drift and diffusion term. By the various methods of stochastic analysis, we derivethe sufficient and necessary conditions of the existence of optimal control.
基金supported by the National Natural Science Foundation of China under Grant Nos.61374080 and 61374067the Natural Science Foundation of Zhejiang Province under Grant No.LY12F03010+1 种基金the Natural Science Foundation of Ningbo under Grant No.2012A610032Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions
文摘This paper studies the strong n(n =—1,0)-discount and finite horizon criteria for continuoustime Markov decision processes in Polish spaces.The corresponding transition rates are allowed to be unbounded,and the reward rates may have neither upper nor lower bounds.Under mild conditions,the authors prove the existence of strong n(n =—1,0)-discount optimal stationary policies by developing two equivalence relations:One is between the standard expected average reward and strong—1-discount optimality,and the other is between the bias and strong 0-discount optimality.The authors also prove the existence of an optimal policy for a finite horizon control problem by developing an interesting characterization of a canonical triplet.
