The improvement of the truncated Euler-Maruyama method for non-Lipschitz stochastic differential equations

IF 1.7 3区数学 Q2 MATHEMATICS, APPLIED

Advances in Computational Mathematics Pub Date : 2024-04-22 DOI:10.1007/s10444-024-10131-w

Weijun Zhan, Yuyuan Li

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.

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非 Lipschitz 随机微分方程的截断 Euler-Maruyama 方法的改进

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。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Advances in Computational Mathematics 数学-应用数学

CiteScore

3.00

自引率

5.90%

发文量

审稿时长

3 months

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.