高非线性随机微分方程的隐式部分截断Euler方法  

IMPLICIT PARTIALLY TRUNCATED EULER-MARUYAMA METHOD FOR HIGHLY NONLINEAR STOCHASTIC DIFFERENTIAL EQUATIONS

作　　者：范振成 Fan Zhencheng(School of Computer and Big Data,Minjiang University,Fuzhou 350108,China)

机构地区：[1]闽江学院计算机与大数据学院,福州350108

出　　处：《计算数学》2024年第4期409-423,共15页Mathematica Numerica Sinica

基　　金：福建省自然科学基金(2021J011031);福建省发树慈善基金会(MFK23013)资助。

摘　　要：高非线性随机微分方程的数值方法可以分为显式和隐式两类方法,通常显式方法的计算量小但稳定性差,隐式方法的稳定性好但计算量大.本文提出一种隐式部分截断Euler方法,证明了它是强收敛和均方稳定的.此外,研究结果表明,对于平移系数含线性函数情况,它与显式部分截断Euler方法计算量相近,而稳定性更好,即兼具显式和隐式方法的优点.The numerical methods of highly nonlinear stochastic differential equations can be divided into two types:explicit methods and implicit methods.In general,the explicit method has cheap computational cost but the stable property is bad,in contrast,the implicit method has good stable property but computational cost is expensive.In this paper,we present the implicit partially truncated Euler-Maruyama method and prove that it is strongly convergent and stable in mean-square sense.In addition,the obtained results show that the presented method has approximate computational cost and better stable property compared with the explicit partially truncated Euler-Maruyama method for the case that the drift coefficient contains a linear function,that is,it posses concurrently the merit of explicit and implicit methods.

关 键 词：随机微分方程 隐式部分截断Euler方法 高非线性条件 强收敛 稳定 

分 类 号：O211.63[理学—概率论与数理统计]