带跳的随机微分方程的Euler折线逼近  

On the Euler Scheme for SDEs with Jumps

作　　者：谢鹏[1] 

机构地区：[1]华中科技大学数学系,武汉430074

出　　处：《应用数学学报》2008年第2期374-381,共8页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(60074033)资助项目.

摘　　要：熟知当随机微分方程的系数不满足Lipschitz条件,而仅满足单调性条件时,我们无法用Picard迭代法证明其解的存在性.Krylov为此对Brown运动驱动的此类方程用Euler折线逼近法证明了解的存在性.本文将Krylov的结果推广到带跳的随机微分方程,证明了Euler折线逼近的收敛性.这一结果是研究带跳的随机发展方程的基础,且对随机微分方程的数值计算有用.It is well known that for stochastic differential equations （SDE） with coefficients which are not Lipschitz but only monotone, one cannot use the Picard iteration to prove the existence of solutions. To overcome this difficulty Krylov used the Euler scheme for such SDEs driven by Brownian motion and proved the existence. In the presernt paper we extend the result of Krylov to SDEs with jumps and proved the convergence of Euler scheme. This will serve as the basis for studying stochastic evolution equations with jumps and will be useful for numerical computation of SDEs.

关 键 词：带跳的随机微分方程 Euler折线 收敛 

分 类 号：O211.63[理学—概率论与数理统计] O177.91[理学—数学]