The aim of this paper is to study backward stochastic differential equation driven by a class of normal martingale. We prove the existence and uniqueness results of the solution under the stochastic Lipschitz condition by mean the martingale representation theorem. In addition, we show that the solution of these equations provides a viscosity solution of the associated system with partial differential equations.

中文翻译：

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由正态鞅驱动的 BSDE

本文的目的是研究一类正态鞅驱动的后向随机微分方程。我们利用鞅表示定理证明了随机Lipschitz条件下解的存在唯一性结果。此外，我们表明这些方程的解提供了具有偏微分方程的关联系统的粘度解。