标题： 具有象记忆的随机线性二次领导者-跟随者微分博弈 显示英文标题

标题： A Stochastic Linear-Quadratic Leader-Follower Differential Game with Elephant Memory

摘要： 本文研究了一种具有大象记忆的随机线性二次领导者-跟随者微分博弈。该模型是通用的，因为领导者和跟随者的状态方程都包含了状态和控制的大象记忆，这些是扩散项的一部分。在某些假设下，通过引入两个Riccati方程和一个特殊的矩阵值方程，推导出了开环Stackelberg策略的状态反馈表示。最后，通过一个涉及具有大象记忆的动态广告问题的例子来说明理论结果。 显示英文摘要

摘要： This paper is concerned with a stochastic linear-quadratic leader-follower differential game with elephant memory. The model is general in that the state equation for both the leader and the follower includes the elephant memory of the state and the control, which are part of the diffusion term. Under certain assumptions, the state feedback representation of the open-loop Stackelberg strategy is derived by introducing two Riccati equations and a special matrix-valued equation. Finally, theoretical results are illustrated by means of an example concerning a dynamic advertising problem with elephant memory.