中文摘要：

利用Bihair不等式、Jensen不等式给出非Lipschitz条件下倒向重随机微分方程解的存在唯一性定理，推广Pardoux和Peng1994年的结论；同时也得到了此类方程在非Lipschitz条件下的比较定理，推广了Shi，Gu和Liu2005年的结果,从而推广倒向重随机微分方程在随机控制及随机偏微分方程在粘性解方面的应用。

英文摘要：

It is proved that a new theorem on the existence and uniqueness of the solution to Backward Doubly Stochastic Differential Equations under a weaker condition than one Lipschitz one by means of the Bihair unequation and Jensen unequation; we also get the comparison theorem to this kind of Backward Doubly Stochastic Differential Equations.