The Convergence of Euler-Maruyama Method of Nonlinear Variable-Order Fractional Stochastic Differential Equations

IF 1.5 4区 工程技术 Q2 MATHEMATICS, APPLIED
Shanshan Xu, Lin Wang null, Wenqiang Wang
{"title":"The Convergence of Euler-Maruyama Method of Nonlinear Variable-Order Fractional Stochastic Differential Equations","authors":"Shanshan Xu, Lin Wang null, Wenqiang Wang","doi":"10.4208/aamm.oa-2021-0222","DOIUrl":null,"url":null,"abstract":". In this paper, we first prove the existence and uniqueness theorem of the solution of nonlinear variable-order fractional stochastic differential equations (VFS-DEs). We futher constructe the Euler-Maruyama method to solve the equations and prove the convergence in mean and the strong convergence of the method. In particular, when the fractional order is no longer varying, the conclusions obtained are consistent with the relevant conclusions in the existing literature. Finally, the numerical experiments at the end of the article verify the correctness of the theoretical results obtained.","PeriodicalId":54384,"journal":{"name":"Advances in Applied Mathematics and Mechanics","volume":null,"pages":null},"PeriodicalIF":1.5000,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Applied Mathematics and Mechanics","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.4208/aamm.oa-2021-0222","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0

Abstract

. In this paper, we first prove the existence and uniqueness theorem of the solution of nonlinear variable-order fractional stochastic differential equations (VFS-DEs). We futher constructe the Euler-Maruyama method to solve the equations and prove the convergence in mean and the strong convergence of the method. In particular, when the fractional order is no longer varying, the conclusions obtained are consistent with the relevant conclusions in the existing literature. Finally, the numerical experiments at the end of the article verify the correctness of the theoretical results obtained.
非线性变阶分数阶随机微分方程Euler Maruyama方法的收敛性
本文首先证明了非线性变阶分数阶随机微分方程(VFS-DEs)解的存在唯一性定理。我们进一步构造了求解方程组的Euler Maruyama方法,并证明了该方法的均值收敛性和强收敛性。特别是,当分数阶数不再变化时,得到的结论与现有文献中的相关结论一致。最后,通过文末的数值实验验证了理论结果的正确性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 求助全文
来源期刊
Advances in Applied Mathematics and Mechanics
Advances in Applied Mathematics and Mechanics MATHEMATICS, APPLIED-MECHANICS
CiteScore
2.60
自引率
7.10%
发文量
65
审稿时长
6 months
期刊介绍: Advances in Applied Mathematics and Mechanics (AAMM) provides a fast communication platform among researchers using mathematics as a tool for solving problems in mechanics and engineering, with particular emphasis in the integration of theory and applications. To cover as wide audiences as possible, abstract or axiomatic mathematics is not encouraged. Innovative numerical analysis, numerical methods, and interdisciplinary applications are particularly welcome.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信