求解随机微分方程混合Euler方法的收敛性  

Convergence of Composite Euler Method for Solving Stochastic Differential Equations

作　　者：王彩霞 张引娣[1] 蒋茜 WANG Caixia;ZHANG Yindi;JIANG Qian(Faculty of Science,Chang’an University,Xi’an 710064,China)

机构地区：[1]长安大学理学院,陕西西安710064

出　　处：《河南科技大学学报（自然科学版）》2019年第2期91-95,110,111,共7页Journal of Henan University of Science And Technology:Natural Science

基　　金：国家自然科学基金项目(11572146;11401044)

摘　　要：通过对求解标量自治随机微分方程的梯形Euler-Maruyama方法进行改进,得到了混合Euler方法。当带有乘性噪音的随机微分方程的两个系数都满足全局Lipschitz条件和线性增长条件时,证明了混合Euler方法的均方强收敛阶是0. 5,并通过数值实验验证了该方法的收敛性。数值实验结果表明:混合Euler方法得到的数值解比梯形Euler-Maruyama方法得到的数值解有更好的逼近效果。By improving the trapezoidal Euler-Maruyama method for solving scalar autonomous stochastic differential equations,the composite Euler method was obtained.When the two coefficients of stochastic differential equation with multiplicative noise both satisfied the global Lipschitz condition and the linear growth condition,it was proved that the mean square strong convergence order of the composite Euler method was0.5,and the convergence of the method was verified by numerical experiments.The results of numerical experiments show that the numerical solution obtained by the composite Euler method has a better approximation effect than the numerical solution obtained by the trapezoidal Euler-Maruyama method.

关 键 词：随机微分方程 混合Euler方法 收敛阶 全局Lipschitz条件 线性增长条件 

分 类 号：O211.63[理学—概率论与数理统计]