带对角线发生器的 G 布朗运动驱动的多维反射后向随机微分方程

Pub Date : 2024-04-26 DOI:10.1007/s10959-024-01334-4

Hanwu Li, Guomin Liu

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摘要

我们考虑了具有对角生成器的由 G 布朗运动驱动的多维反射反向随机微分方程（G-BSDE）的好求问题。我们提供了包括惩罚法和 Picard 迭代论证在内的两种方法来证明解的存在性和唯一性。我们还研究了它与全非线性 PDE 系统的障碍问题之间的联系。

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Multi-dimensional Reflected Backward Stochastic Differential Equations Driven by G-Brownian Motion with Diagonal Generators

We consider the well-posedness problem of multi-dimensional reflected backward stochastic differential equations driven by G-Brownian motion (G-BSDEs) with diagonal generators. Two methods, including the penalization method and the Picard iteration argument, are provided to prove the existence and uniqueness of the solutions. We also study its connection with the obstacle problem of a system of fully nonlinear PDEs.

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