LINEAR QUADRATIC STOCHASTIC TWO-PERSON ZERO-SUM DIFFERENTIAL GAMES IN AN INFINITE HORIZON
LINEAR QUADRATIC STOCHASTIC TWO-PERSON ZERO-SUM DIFFERENTIAL GAMES IN AN INFINITE HORIZON
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无限视野中的线性二次随机二人零和微分博弈
DOI：
10.1051/cocv/2015024
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
Zhang Shuguang
中科院分区：
文献类型：
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作者：
Sun Jingrui;Yong Jiongmin;Zhang Shuguang
本文研究无限时间域上一类线性二次随机二人零和常系数微分对策。介绍了开环鞍点和闭环鞍点。在一定的稳定化条件下，用代数Riccati方程的可解性刻画了闭环鞍点的存在性。一个重要的结果是一类线性倒向随机微分方程解在无限水平上的唯一性。
This paper is concerned with a linear quadratic stochastic two-person zero-sum differential game with constant coefficients in an infinite time horizon. Open-loop and closed-loop saddle points are introduced. The existence of closed-loop saddle points is characterized by the solvability of an algebraic Riccati equation with a certain stabilizing condition. A crucial result makes our approach work is the unique solvability of a class of linear backward stochastic differential equations in an infinite horizon.