{"title":"The improvement of the truncated Euler-Maruyama method for non-Lipschitz stochastic differential equations","authors":"Weijun Zhan, Yuyuan Li","doi":"10.1007/s10444-024-10131-w","DOIUrl":null,"url":null,"abstract":"<div><p>This paper is concerned with the numerical approximations for stochastic differential equations with non-Lipschitz drift or diffusion coefficients. A modified truncated Euler-Maruyama discretization scheme is developed. Moreover, by establishing the criteria on stochastic C-stability and B-consistency of the truncated Euler-Maruyama method, we obtain the strong convergence and the convergence rate of the numerical method. Finally, numerical examples are given to illustrate our theoretical results.</p></div>","PeriodicalId":50869,"journal":{"name":"Advances in Computational Mathematics","volume":"50 3","pages":""},"PeriodicalIF":1.7000,"publicationDate":"2024-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Computational Mathematics","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10444-024-10131-w","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
This paper is concerned with the numerical approximations for stochastic differential equations with non-Lipschitz drift or diffusion coefficients. A modified truncated Euler-Maruyama discretization scheme is developed. Moreover, by establishing the criteria on stochastic C-stability and B-consistency of the truncated Euler-Maruyama method, we obtain the strong convergence and the convergence rate of the numerical method. Finally, numerical examples are given to illustrate our theoretical results.
本文关注具有非 Lipschitz 漂移或扩散系数的随机微分方程的数值近似。本文提出了一种改进的截断欧拉-马鲁山离散化方案。此外，通过建立截断式 Euler-Maruyama 方法的随机 C 稳定性和 B 一致性准则，我们得到了数值方法的强收敛性和收敛速率。最后，我们给出了数值示例来说明我们的理论结果。
期刊介绍：
Advances in Computational Mathematics publishes high quality, accessible and original articles at the forefront of computational and applied mathematics, with a clear potential for impact across the sciences. The journal emphasizes three core areas: approximation theory and computational geometry; numerical analysis, modelling and simulation; imaging, signal processing and data analysis.
This journal welcomes papers that are accessible to a broad audience in the mathematical sciences and that show either an advance in computational methodology or a novel scientific application area, or both. Methods papers should rely on rigorous analysis and/or convincing numerical studies.
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