In this paper, we first recall some classical results concerning the relationship among ordinary differential equations (ODEs), partial DEs (PDEs) and stochastic DEs (SDEs), known as the Hamilton-Jacobi theory and Feynman-Kac formula. Then the results involving optimal control, and the recent results of backward SDEs (BSDEs) and/or forward-backward stochastic differential equations (FBSDEs) are presented.
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Jiongmin Yong (2002) studied this question.
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