• 论文 •

### 多项Caputo分数阶随机微分方程的Euler-Maruyama方法

1. 扬州大学数学科学学院, 扬州 225002
• 收稿日期:2020-12-15 出版日期:2022-07-14 发布日期:2022-08-03
• 通讯作者: 黄健飞,Email:jfhuang@lsec.cc.ac.cn.
• 基金资助:
国家自然科学基金项目(11701502,11871065)和江苏省自然科学基金项目(BK20201427)资助.

Huo Zhengyang, Zhang Jingna, Huang Jianfei. EULER-MARUYAMA SCHEME FOR MULTI-TERM CAPUTO FRACTIONAL STOCHASTIC DIFFERENTIAL EQUATIONS[J]. Mathematica Numerica Sinica, 2022, 44(3): 354-367.

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

Huo Zhengyang, Zhang Jingna, Huang Jianfei

1. College of Mathematical Sciences, Yangzhou University, Yangzhou 225002, China
• Received:2020-12-15 Online:2022-07-14 Published:2022-08-03

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 is $\alpha_{m}-\alpha_{m-1}$ order strong convergence, where $\alpha_{i},i=1,\cdots,m$, is the fractional order with $\frac{1}{2}<\alpha_{1}<\alpha_{2}<\cdots<\alpha_{m}<1$. Finally, numerical experiments are given to support the theoretical results of our EM method.

MR(2010)主题分类:

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