MAXIMUM PRINCIPLE FOR STOCHASTIC OPTIMAL CONTROL PROBLEM WITH DISTRIBUTED DELAYS  

作　　者：Qixia ZHANG 张启侠(School of Mathematical Sciences,University of Jinan,Jinan 250022,China)

机构地区：[1]School of Mathematical Sciences,University of Jinan,Jinan 250022,China

出　　处：《Acta Mathematica Scientia》2021年第2期437-449,共13页数学物理学报（B辑英文版）

基　　金：supported by the National Natural Science Foundation of China(11701214);Shandong Provincial Natural Science Foundation,China(ZR2019MA045).

摘　　要：This paper is concerned with a Pontryagin's maximum principle for the stochastic optimal control problem with distributed delays given by integrals of not necessarily linear functions of state or control variables.By virtue of the duality method and the generalized anticipated backward stochastic differential equations,we establish a necessary maximum principle and a sufficient verification theorem.In particular,we deal with the controlled stochastic system where the distributed delays enter both the state and the control.To explain the theoretical results,we apply them to a dynamic advertising problem.

关 键 词：Distributed delay generalized anticipated backward stochastic differential equations optimal control maximum principle 

分 类 号：O211.63[理学—概率论与数理统计] O232[理学—数学]