In this paper, we give a probabilistic interpretation for solutions to the Neumann boundary problems for a class of semi-linear parabolic partial differential equations (PDEs for short) with singular non-linear divergence terms. This probabilistic approach leads to the study on a new class of backward stochastic differential equations (BSDEs for short). A connection between this class of BSDEs and semi-linear PDEs is established.

中文翻译：

---

带散度项的抛物型偏微分方程的Neumann边界问题

在本文中，我们给出了一类具有奇异非线性散度项的半线性抛物型偏微分方程（简称PDE）的Neumann边界问题解的概率解释。这种概率方法导致了对一类新型的后向随机微分方程（简称BSDE）的研究。在此类BSDE与半线性PDE之间建立了连接。