论文标题
双重反映了由G-Brownian动作和完全非线性PDE的双障碍物驱动的后向SDE
Doubly Reflected Backward SDEs Driven by G-Brownian Motions and Fully Nonlinear PDEs with Double Obstacles
论文作者
论文摘要
在本文中，我们引入了一种新方法，以研究由G-Brownian运动（G-BSDE）驱动的双重反映的后退随机微分方程。我们的方法涉及通过一个受惩罚的反射G-BSDE的家族近似溶液，而单调较低的障碍物较低。通过采用这种方法，我们建立了具有最弱的已知条件的双重反映G-BSDE的解决方案的良好性，并首次与双重非线性偏微分方程和双重障碍物发现了其与完全非线性的偏微分方程的关系。
In this paper, we introduce a new method to study the doubly reflected backward stochastic differential equation driven by G-Brownian motion (G-BSDE). Our approach involves approximating the solution through a family of penalized reflected G-BSDEs with a lower obstacle that are monotone decreasing. By employing this approach, we establish the well-posedness of the solution of the doubly reflected G-BSDE with the weakest known conditions, and uncover its relationship with the fully nonlinear partial differential equation with double obstacles for the first time.
