高维倒向随机微分方程比较定理

Comparison Theorem for Multidimensional Backward Stochastic Differential Equations

  • 摘要: 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,曹志刚和严加安给出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.

     

    Abstract: 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.

     

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