Numerical Solutions for Optimal Control of Stochastic Kolmogorov Systems  

作　　者：YIN George WEN Zhexin QIAN Hongjiang NGUYEN Huy 

机构地区：[1]Department of Mathematics,University of Connecticut,Storrs,CT 06269,USA [2]School of Mathematics and Statistics,Central South University,Changsha 410083,China [3]Department of Mathematics,Wayne State University,Detroit,MI 48202,USA

出　　处：《Journal of Systems Science & Complexity》2021年第5期1703-1722,共20页系统科学与复杂性学报（英文版）

基　　金：ARO W911NF1810334;NSF under EPCN 1935389;the National Renewable Energy Laboratory(NREL)。

摘　　要：This work is concerned with controlled stochastic Kolmogorov systems.Such systems have received much attention recently owing to the wide range of applications in biology and ecology.Starting with the basic premise that the underlying system has an optimal control,this paper is devoted to designing numerical methods for approximation.Different from the existing literature on numerical methods for stochastic controls,the Kolmogorov systems take values in the first quadrant.That is,each component of the state is nonnegative.The work is designing an appropriate discrete-time controlled Markov chain to be in line with(locally consistent)the controlled diffusion.The authors demonstrate that the Kushner and Dupuis Markov chain approximation method still works.Convergence of the numerical scheme is proved under suitable conditions.

关 键 词：Controlled diffusion controlled Markov chain Kolmogorov equation numerical approximation 

分 类 号：O211.6[理学—概率论与数理统计] O232[理学—数学]