带噪声记忆的非零和随机微分博弈问题的充分最大值原理  

Sufficient maximum principle for one kind of nonzero-sum stochastic differential game involving noisy memory

作　　者：张峰[1] 梁嘉玮 ZHANG Feng;LIANG Jiawei(School of Statistics and Mathematics,Shandong University of Finance and Economics,Jinan 250014,Shandong,China)

机构地区：[1]山东财经大学统计与数学学院,山东济南250014

出　　处：《山东大学学报（理学版）》2024年第10期46-52,共7页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助项目(12171279)。

摘　　要：研究一类非零和随机微分博弈问题,其主要特点是状态变量和控制变量可以带有多种形式的时滞。状态变量可以带有分布时滞、离散时滞与噪声记忆,控制变量可以带有分布时滞与离散时滞。控制域为凸集。利用最大值原理方法建立该博弈问题的均衡点所满足的充分条件。最后研究一个例子,给出均衡点的显式表达式。One nonzero-sum stochastic differential game is considered,whose main feature is that several kinds of delays of the state and the control are involved.The state process can contain distributed delays,discrete delays,and noisy memory,and control processes can contain distributed delays and discrete delays.The control domains are convex sets.Sufficient conditions for the equilibrium point of the game are established by means of the stochastic maximum principle.Finally,an illustrative example is considered for which the equilibrium point is obtained in explicit form.

关 键 词：非零和随机微分博弈 时滞 噪声记忆 均衡点 最大值原理 

分 类 号：O232[理学—运筹学与控制论]