We obtain upper and lower Gaussian density estimates for the law of each component of the solution to a one-dimensional fully coupled forward-backward SDE (FBSDE). Our approach relies on the link between FBSDEs and quasilinear parabolic PDEs, and is fully based on the use of classical results on PDEs rather than on manipulation of FBSDEs, compared to other papers on this topic. This essentially simplifies the analysis.

中文翻译：

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全耦合前向后向 SDE 解的高斯密度估计

我们获得了对一维完全耦合的前向后向 SDE (FBSDE) 的解的每个分量的定律的高斯密度估计值和下高斯密度估计值。与该主题的其他论文相比，我们的方法依赖于 FBSDE 和拟线性抛物线 PDE 之间的联系，并且完全基于对 PDE 的经典结果的使用，而不是基于 FBSDE 的操作。这实质上简化了分析。