中立型随机时滞微分方程截断Milstein数值解的强收敛性  

Strong convergence of the truncated Milstein numerical solution of neutral stochastic delay differential equations

作　　者：李琛 尤苏蓉[1] LI Chen;YOU Surong(College of Science, Donghua University, Shanghai 201620, China)

机构地区：[1]东华大学理学院,上海201620

出　　处：《纺织高校基础科学学报》2021年第1期74-83,共10页Basic Sciences Journal of Textile Universities

基　　金：上海自然科学基金资助项目(17ZR1401300)。

摘　　要：研究非线性系数的Milstein中立型随机时滞微分方程数值解的收敛性问题。将截断思想和Milstein数值格式结合,对有高度非线性系数的中立型随机时滞微分方程,构建了截断Milstein数值格式。在局部Lipschitz条件及Khasminskii条件下,证明了中立型随机时滞微分方程截断Milstein数值解Lp强收敛于精确解。针对一个具体的中立型随机时滞微分方程,使用数值模拟验证了结论的正确性。The convergence of numerical solutions for Milstein Neutral Stochastic Delay Differential Equations with nonlinear coefficients is studied.A truncated Milstein numerical scheme is constructed for neutral stochastic delay differential equations with highly nonlinear coefficients by combining the truncation idea with the Milstein numerical scheme.Under the local Lipschitz condition and Khasminskii condition,it is proved that the truncated Milstein numerical solution Lp converges strongly to the exact solution for a neutral stochastic delay differential equation.The correctness of the conclusion is verified by numerical simulation for a specific neutral stochastic delay differential equation.

关 键 词：中立型随机微分方程 强收敛 Khasminskii条件 截断Milstein方法 

分 类 号：O29[理学—应用数学]