{"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.
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.