高维倒向随机微分方程比较定理

倒向随机微分方程由Pardoux和彭实戈首先提出，彭实戈给出了一维BSDE的比较定理，周海滨将其推广到了高维情形．毛学荣将倒向随机微分方程解的存在唯一性定理推广到非Lipschitz系数情况，曹志刚和严加安给了相应的一维比较定理．本文将曹志刚和严加安的比较定理推广到高维情形．

Comparison Theorem for Multidimensional Backward Stochastic Differential Equations

Backward stochastic differential equations (BSDE, for short) were first introduced by Pardoux-Peng, and a comparison theorem for solutions of one-dimensional BSDE were established by Peng, which Zhou has generalized to the multi-dimensional case. Mao has generalized the existence and unique theorem to the case of non-Lipschitzian coefficients, and then Cao-Yan established a comparison theorem for solutions of one-dimensional case. In the present paper, we generalize Cao-Yan's comparison theorem to the multi-dimensional case.