中立型随机泛函微分方程截断Euler-Maruyama数值解的均方指数稳定分析  

Analysis on mean-square exponential stability ofthe truncated Euler-Maruyama numerical solutionsfor neutral stochastic functional differential equations

作　　者：王子丰 尤苏蓉[1] WANG Zifeng;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：《东华大学学报（自然科学版）》2021年第1期125-130,共6页Journal of Donghua University(Natural Science)

基　　金：上海自然科学基金资助项目(17ZR1401300)。

摘　　要：为研究截断Euler-Maruyama数值方法对有高度非线性特征的中立型随机泛函微分方程的适用性和稳定性,建立适用于此类方程的截断Euler-Maruyama数值解。给出截断Euler-Maruyama数值解均方指数稳定的条件,并证明在系数满足局部Lipschitz条件、压缩映射条件以及Khasminskii条件下,该中立型随机泛函微分方程的解析解是均方指数稳定的,同时,其截断Euler-Maruyama数值解也具有均方指数稳定的特征。针对一个具体中立型随机泛函微分方程,采用数值模拟验证了上述结论的正确性。The truncated Euler-Maruyama numerical solution for a neutral stochastic functional differential equation with highly nonlinear coefficients was constructed to study the applicability and stability of the numerical solution.The condition for mean-square exponential stability of the truncated Euler-Maruyama solution was given.The result shows that when the coefficients satisfy the local Lipschitz condition,contractive mapping and Khasminskii condition,the analytic solution will be mean-square exponentially stable.Meanwhile,the truncated Euler-Maruyama numerical solution will be exponentially stable too.On the basis of a specific neutral stochastic functional differential equation,the numerical simulation was used to verify the correctness of the result.

关 键 词：中立型随机泛函方程 均方指数稳定 截断Euler-Maruyama数值解 Khasminskii条件 

分 类 号：O29[理学—应用数学]