非Lipschitz条件下由连续半鞅驱动的倒向随机微分方程的解（英文）  

The solution of BSDEs driven by continuous semi-martingales under non-Lipschitz condition

作　　者：李师煜[1] 李文学[1] 李华灿[1] 

机构地区：[1]江西理工大学理学院,赣州341000

出　　处：《黑龙江大学自然科学学报》2015年第4期485-489,共5页Journal of Natural Science of Heilongjiang University

基　　金：Supported by the National Natural Science Foundation of China(11461032;11401267;11326238);the Natural Science Foundation of Jiangxi Province(20151bab201013);the Youth Foundation of Jiangxi Provincial Education Department(GJJ13376);the Research Foundation of Jiangxi University of Science and Techology(JxxJ bs1 2002;nsfj 2015-K17)

摘　　要：经典的倒向随机微分方程以布朗运动为干扰源。研究由连续半鞅驱动的倒向随机微分方程,在生成元满足一定的非Lipschitz条件下,通过构造一个Picard序列的方法,利用It^o公式、Lebesgue控制收敛定理和常微分方程的比较定理,证明其解是存在并且唯一的,对经典倒向随机微分方程进行了实质性的推广。The classical backward stochastic differential equations are taken the Brownian motion as the noise source. The backward stochastic equations driven by continuous semi-martingale are studied. A general existence and uniqueness result of the solutions is established under certain non-Lipschitz condition on the generator by constructing Picard sequence and using Ito^ formula,Lebesgue＇s dominated convergence theorem and the comparison of ordinary differential equation. This conducts a substantial extension of the classical backward stochastic differential equations.

关 键 词：倒向随机微分方程 连续半鞅 非Lipschitz系数 存在性 唯一性 

分 类 号：O211.6[理学—概率论与数理统计]