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.