Abstract This paper explores the relationship between non-Markovian fully coupled forward–backward stochastic systems and path-dependent PDEs. The definition of classical solution for the path-dependent PDE is given within the framework of functional Itô calculus. Under mild hypotheses, we prove that the forward–backward stochastic system provides the unique classical solution to the path-dependent PDE.

中文翻译：

---

非马尔可夫全耦合前向后向随机系统和路径相关 PDES 的经典解

摘要 本文探讨了非马尔可夫完全耦合的前向后向随机系统与路径相关的偏微分方程之间的关系。在泛函 Itô 演算的框架内给出了路径依赖 PDE 的经典解的定义。在温和的假设下，我们证明了前向-后向随机系统为路径依赖的偏微分方程提供了独特的经典解。