非Lipschitz条件下由连续局部鞅驱动的倒向随机微分方程  

Backward stochastic differential equations driven by continuous local martingale under non-Lipschitz condition

作　　者：李师煜[1] 李文学[1] 高武军[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》2014年第3期335-339,共5页Journal of Natural Science of Heilongjiang University

基　　金：国家自然科学基金资助项目(11326238);江西省教育厅青年科学基金资助项目(GJJ13376)

摘　　要：经典的倒向随机微分方程是由布朗运动驱动的,而布朗运动是一种非常特殊的随机过程,致使倒向随机微分方程的应用受到相当大的限制。研究以连续局部鞅为干扰源的倒向随机微分方程。在生成元满足Mao论文中非Lipschitz条件下,通过构造一个Picard序列,利用Gronwall不等式、It^o公式和Bihari’s不等式,证明了其解存在且唯一。The classical backward stochasticdifferential equations（BSDE） is driven by the Brownian motion, but the Brownmotion is one kind of special stochastic process, which causes the classical BSDE theory to receive certain limit in applications. The backward stochasticdifferential equation is taken continuous local martingale as the noise source isconsidered. The existence and uniqueness theorem under non-Lipschitz condition of Mao on the generator by construction of Picard sequence, Gronwall inequality, Itoformula and Bihari＇ s inequality is obtained.

关 键 词：倒向随机微分方程 连续局部鞅 存在性 唯一性 

分 类 号：O211.6[理学—概率论与数理统计]