论文标题
对角发电机的FBSDE的统一方法的统一方法
A unified approach to global solvability for FBSDEs with diagonal generators
论文作者
论文摘要
在本文中，我们研究了具有对角Lipschitz，二次或超质量发生器的多维前向随机微分方程（FBSDE）的全球可溶性。在某种“单调性”条件下，我们提供了一种统一的方法，该方法表明存在一个脱钩场，其空间变量均匀地lipschitz。该去耦场与相关特征BSDE的有界解决方案密切相关。对于Lipschitz案例，我们提供一些扩展名，并调查$ l^p $ - 解决方案和$ l^p $估计。我们的结果对Yong提出的一个问题提供了积极的答案（Banach CenterPubl。122：255-286，2020）。研究了随机最佳控制和随机差异游戏的应用。
In this paper, we study the global solvability of multidimensional forward-backward stochastic differential equations (FBSDEs) with diagonally Lipschitz, quadratic or super-quadratic generators. Under a certain "monotonicity" condition, we provide a unified approach which shows that there exists a decoupling field that is uniformly Lipschitz in its spatial variable. This decoupling field is closely related to bounded solution to an associated characteristic BSDE. For Lipschitz case, we provide some extensions and investigate $L^p$-solution and $L^p$ estimates. Our results gives a positive answer to a question proposed in Yong (Banach Center Publ. 122: 255-286, 2020). Applications to stochastic optimal controls and stochastic differential games are investigated.
