多项Caputo分数阶随机微分方程的Euler-Maruyama方法  

EULER-MARUYAMA SCHEME FOR MULTI-TERM CAPUTO FRACTIONAL STOCHASTIC DIFFERENTIAL EQUATIONS

作　　者：霍振阳 张静娜 黄健飞 Huo Zhengyang;Zhang Jingna;Huang Jianfei(College of Mathematical Sciences,Yangzhou University,Yangzhou 225002,China)

机构地区：[1]扬州大学数学科学学院,扬州225002

出　　处：《计算数学》2022年第3期354-367,共14页Mathematica Numerica Sinica

基　　金：国家自然科学基金项目(11701502,11871065);江苏省自然科学基金项目(BK20201427)资助

摘　　要：本文主要研究了一类多项Caputo分数阶随机微分方程的Euler-Maruyama(EM)方法,并证明了其强收敛性.具体地,我们首先构造了求解多项Caputo分数阶随机微分方程初值问题的EM方法,然后证明分数阶导数的指标满足1/2<α_(1)<α_(2)<…<α_(m)<1时,该方法是α_(m)-α_(m-1)阶强收敛的.文末的数值试验验证了理论结果的正确性.In this paper,we study the Euler-Maruyama(EM)method for a class of multi-term Caputo fractional stochastic differential equations,and prove its strong convergence.Specifically,we first construct the EM method for the initial value problem of multi-term Caputo fractional stochastic differential equations,and then we prove that the method isα_(m)-α_(m-1) order strong convergence,whereαi,i=1,…,m,is the fractional order with 1/2<α_(1)<α_(2)<…<α_(m)<1.Finally,numerical experiments are given to support the theoretical results of our EM method.

关 键 词：分数阶随机微分方程 多项Caputo导数 EULER-MARUYAMA方法 强收敛性 

分 类 号：O211.63[理学—概率论与数理统计]