Stochastic Differential Games: A Sampling Approach via FBSDEs
Stochastic Differential Games: A Sampling Approach via FBSDEs
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DOI：
10.1007/s13235-018-0268-4
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发表时间：
2018-06
影响因子：
1.5
通讯作者：
Ioannis Exarchos;Evangelos A. Theodorou;P. Tsiotras
中科院分区：
文献类型：
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作者：
Ioannis Exarchos;Evangelos A. Theodorou;P. Tsiotras
这项工作的目的是提出一种基于抽样的算法，用于求解各类随机微分对策。该方法的基础在于将对策解表示为一对解耦的前向和后向随机微分方程组。根据Feynman-Kac引理的非线性形式，得到了每类非线性Hamilton-Jacobi-Isaacs方程解的概率表示。这些表示形式是解耦的FBSDE系统，可以用数值方法求解。
The aim of this work is to present a sampling-based algorithm designed to solve various classes of stochastic differential games. The foundation of the proposed approach lies in the formulation of the game solution in terms of a decoupled pair of forward and backward stochastic differential equations (FBSDEs). In light of the nonlinear version of the Feynman–Kac lemma, probabilistic representations of solutions to the nonlinear Hamilton–Jacobi–Isaacs equations that arise for each class are obtained. These representations are in form of decoupled systems of FBSDEs, which may be solved numerically.