具有非Lipschitz和非增长条件的带跳倒向随机微分方程

本文研究一类带Poisson跳的倒向随机微分方程。在方程的系数满足非增长条件和非Lipschitz条件下,讨论方程适应解的存在唯一性和稳定性。为了证明解的存在性,首先通过函数变换,构造出一逼近序列,然后运用推广的Bihari不等式和Lebesgue控制收敛定理证明该逼近序列是收敛的,得到逼近序列的极限就是方程的适应解。解的唯一性和稳定性主要运用了Bihari不等式和推广的Bihari不等式来进行证明。

Backward Stochastic Differential Equations with Poisson Jumps under Non- Lipschitz and Non- growth Condition

In this paper, we consider the adapted solutions of the backward stochastic differential equations with Poisson jmnps. When the coefficientfsatisfies non -growth condition and non -Lipschitz condition, we discuss the existence of the adapted solutions of the backward stochastic differential equations. Using transformation of function, we construct an approximating sequence. With the help of extended Bihari inequality and Lebesgue dominated convergence theorem, we can show that the approximating sequence converges to a limit, which satisfies the backward sto- chastic differential equations. By the Bihari inequality and extended Bihari inequality, we prove the uniqueness and stability of the solutions of the backward stochastic differential equations.