具有拟Hlder连续生成元的倒向随机微分方程的可积解

Integrable Solutions to BSDEs with Quasi-Holder Continuous Generators

本文证明了具有可积参数的一维倒向随机微分方程解的一个新的存在唯一性结果,其中生成元g关于y满足Osgood条件且关于z是拟Hlder连续的(这里可以不是Hlder连续的).利用Tanaka公式及Girsanov变换建立BSDE的L^1解的一个比较定理,从而得到解的唯一性.利用单调逼近方法给出生成元g的一个一致逼近序列进而构造出BSDE的L^1解的一个序列,然后证明其极限即为所需的解,从而证明解的存在性.

This paper established a new existence and uniquness result for solutions to one dimensional backward stochastic differential equations with only integrable parameters, where the generators satisfy the Osgood condition in y, and quasi-HSlder continuous in z （it maybe not HSlder continuous in z）. By Tanaka＇s formula and Girsanov＇s theorem we established a comparison theorem of solutions in L1 to BSDEs, from which the uniqueness follows. By monotonic approximation method we constructed a sequence of generators and then proved the limitation of the solutions to this sequence is the desired solution. This proved the existence.