【摘要】 本文讨论了倒向随机微分方程在f(t,y,z)满足:(?)N>0,(?)CN0,LN>0,使得对任意y1,y2∈Rn,z1,z2∈Rn×d 当0≤|y1|,|y2|,|z1|,|z2|≤N时,有 |f,(s,y1,z1)-f(s,y2,z2)|2≤CNK(t,|y1-y2|2)+LN|z1-z2|2 的非Lipschitz条件时解的存在性和唯一性。2003年,王赢、王向荣证明了一类倒向随机微分方程解的存在唯一性,我们使用函数逼近法,得到一列满足王赢,王向荣文中条件的倒向随机微分方程,因而每个方程均有唯一解,然后通过取极限的方法证明我们所讨论的方程有唯一解(Y Z),从而推广了他们的结果。更多还原

【Abstract】 We study the existence and uniqueness of solutions on the following BSDEs: where f(t,y,z) satisfies non-Lipschitz condition: (?)N>0,(?)CN>0,LN>0, when y1,y2 ∈Rn, z1,z2∈rn×d and 0≤|y1|,|y2|,|z1|,|z2|≤N, |f(s,y1,z1)-f(s,y2,z2)|2≤CNK(t,|y1-y2|2)+LN|z1-z2|2. In 2003, Wang Ying and Wang Xiangrong proved existence and uniqueness of the locally and globally adapted solutions on a class of BSDEs. We extend their results. Firstly, we construct a serial of BSDEs satisfying those conditions in their paper, hence each equation has a unique solution. Finally, we prove that our equation has a unique solution by taking a limit on the equations serial.更多还原