随机微分方程的截断Caratheodory数值方法  

Truncated Caratheodory numerical method for stochastic differential equtions

作　　者：沈庆庆 胡良剑[1] SHEN Qingqing;HU Liangjian(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：《应用数学与计算数学学报》2018年第4期786-796,共11页Communication on Applied Mathematics and Computation

基　　金：国家自然科学基金资助项目(11471071)

摘　　要：研究了随机微分方程的截断Caratheodory数值解的收敛性.Caratheodory方法是随机微分方程的一种数值求解方法,但当全局Lipschitz条件或线性增长条件不满足时,收敛性往往不能得到保证.在局部Lipschitz条件和Khasminskii型增长条件下,证明了截断Caratheodory数值解的收敛性.This paper focuses on the convergence of the truncated Caratheodory numerical solution of the stochastic differential equation.The Caratheodorymethod is a numerical method for stochastic differential equations.However,when the equations do not satisfy the global Lipschitz condition or the linear growth condi-tion,the convergence cannot be guaranteed.This paper mainly proves the conver-gence of the truncated Caratheodory numerical solution under the local Lipschitz condition and the Khasminskii condition.

关 键 词：局部LIPSCHITZ条件 Khasminskii型增长条件 截断Caratheodory数值解 收敛性 

分 类 号：O211.63[理学—概率论与数理统计]