部分信息下时滞平均场随机微分方程的最大值原理  

Partially information of the maximum value of mean field stochastic differential delay equation under the principle

作　　者：赵婧帆 邢蕾 赵明明 ZHAO Jingfan;XING Lei;ZHAO Mingming(School of Mathematics&Statistics,Changchun University of Technology,Changchun 130012,China)

机构地区：[1]长春工业大学数学与统计学院,吉林长春130012

出　　处：《长春工业大学学报》2024年第6期550-556,共7页Journal of Changchun University of Technology

基　　金：吉林省教育厅科学研究项目(JJKH20230743KJ)。

摘　　要：研究部分信息下时滞平均场随机微分方程的最大值原理。将平均场理论与时滞系统引入随机微分方程,构造时滞平均场型随机微分方程与平均场型效用函数。满足Lipschitz的条件下,得到时滞平均场随机微分方程解的存在唯一性定理。在控制集为凸集的假设条件下,利用变分法给出部分信息下时滞平均场随机微分方程的最大值原理及证明。Studied the partial information of the maximum value of average field stochastic differential delay equation based on partial information.By introducing mean-field theory and time-delay systems into stochastic differential equations,we have constructed time-delayed mean-field type stochastic differential equations and mean-field type utility functions.Average delay in satisfy Lipschitz condition,existence and uniqueness theorem of solutions of stochastic differential equations.Furthermore,under the assumption that the control set is a convex set,we have used the variational method to derive the maximum principle of time-delayed mean-field stochastic differential equations based on partial information and provided its proof.

关 键 词：时滞平均场 解的存在唯一性 变分法 随机最大值原理 

分 类 号：O211.63[理学—概率论与数理统计]