中文摘要：

经典的倒向随机微分方程以布朗运动为干扰源。研究由连续半鞅驱动的倒向随机微分方程,在生成元满足一定的非Lipschitz条件下,通过构造一个Picard序列的方法,利用It^o公式、Lebesgue控制收敛定理和常微分方程的比较定理,证明其解是存在并且唯一的,对经典倒向随机微分方程进行了实质性的推广。

英文摘要：

The classical backward stochastic differential equations are taken the Brownian motion as the noise source. The backward stochastic equations driven by continuous semi-martingale are studied. A general existence and uniqueness result of the solutions is established under certain non-Lipschitz condition on the generator by constructing Picard sequence and using Ito^ formula,Lebesgue＇s dominated convergence theorem and the comparison of ordinary differential equation. This conducts a substantial extension of the classical backward stochastic differential equations.