带时滞随机泛函微分方程的Split-step算法  

Split-step Method for Stochastic Delay Functional Differential Equations

作　　者：张丹[1] 秦衍[1] 

机构地区：[1]华东理工大学数学系,上海200237

出　　处：《华东理工大学学报（自然科学版）》2015年第6期863-870,共8页Journal of East China University of Science and Technology

摘　　要：针对一类带有泊松跳的时变时滞随机泛函微分方程,基于Euler-Maruyama算法,给出了Split-step算法。在带跳时滞随机泛函微分方程的系数满足全局Lipschitz条件、线性增长条件和初值函数具有Hlder连续性的条件下,证明了文中的Split-step算法在均方意义下以0.5阶矩收敛。最后通过几个实例进行了数值模拟,验证了算法的有效性。The Split-step method to stochastic functional differential equations with Poisson jumps and variable delay is introduced in this paper,based on Euler-Maruyama method.And it is proved that the convergence of the Split-step numerical solutions for the stochastic functional differential equations has order 0.5in the mean-square sense under the global Lipschitz condition,the linear growth condition and the continuity of initial data.Some numerical experiments are simulated to testify the performance and the effectiveness of the method.

关 键 词：泊松跳 时滞 Split-step算法 均方收敛 

分 类 号：O211.63[理学—概率论与数理统计]