非Lipschitz条件下由Lévy过程驱动的倒向随机微分方程解的存在唯一及其稳定性(英文)  

Existence, Uniqueness and Stability of Solutions for BSDE Driven by Lévy Processes under Non-Lipschitz Condition

作　　者：任永[1,2] 胡兰英[1] 夏宁茂[2] 

机构地区：[1]安徽师范大学数学系,安徽芜湖241000 [2]华东理工大学数学系,上海200237

出　　处：《应用数学》2007年第2期307-315,共9页Mathematica Applicata

基　　金：Supported by the Key Science and Technology Project of Ministry of Education(207407); NSF of Anhui Educational Bureau(2006kj251B);the Special Project Grants of AnhuiNormal University (2006xzx08)

摘　　要：本文研究了由满足某种矩条件下Lévy过程相应的Teugel鞅及与之独立的布朗运动驱动的倒向随机微分方程,给出了飘逸系数满足非Lipschitz条件下解的存在唯一及稳定性结论.解的存在性是通过Picard迭代法给出的.解的L2收敛性是在飘逸系数弱于L2收敛意义下所得到的.We deal with backward stochastic differential equations （BSDEs in short） driven by Teugel＇s martingales associated with Levy process satisfying some moment condition and an independent Brownian motion. We derive the existence, uniqueness and stability of solutions for these equations under non-Lipschitz condition on the coefficients. And the existence of the solutions is obtained by a Picard-type iteration. The strong L^2 convergence of solutions is derived under a weaker condition than the strong L^2 convergence on the coefficients.

关 键 词：倒向随机微分方程 LEVY过程 Teugel 鞅 

分 类 号：O211.63[理学—概率论与数理统计]