The Truncated Euler–Maruyama Method for Caputo Fractional Stochastic Differential Equations

IF 2.1 3区数学 Q1 MATHEMATICS, APPLIED

Mathematical Methods in the Applied Sciences Pub Date : 2025-02-14 DOI:10.1002/mma.10801

Jiajun Liu, Qiu Zhong, JianFei Huang

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引用次数: 0

Abstract

In this paper, we firstly construct the truncated Euler–Maruyama (EM) method for Caputo fractional stochastic differential equations (Caputo FSDEs) with the local Lipschitz condition and the Khasminskii-type condition on drift and diffusion functions. After that, the boundedness and strong convergence of the numerical solutions are theoretically analyzed. Moreover, the strong convergence order of this presented truncated EM method is proved as $α - 0.5$ , where $α$ denotes the order of Caputo derivative and $0.5 < α < 1$ . In the end, numerical experiments are demonstrated to confirm the correctness of the theoretical results.

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Caputo分数阶随机微分方程的截断Euler-Maruyama方法

本文首先构造了具有漂移函数和扩散函数的局部Lipschitz条件和khasminskii型条件的Caputo分数阶随机微分方程（Caputo FSDEs）的截断Euler-Maruyama （EM）方法。然后，从理论上分析了数值解的有界性和强收敛性。并证明了该方法的强收敛阶为α−0。5 $$ \alpha -0.5 $$，其中α $$ \alpha $$为卡普托导数阶数，为0。5 ＆lt；α ＆lt；1 $$ 0.5<\alpha <1 $$。最后通过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。

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来源期刊

Mathematical Methods in the Applied Sciences 数学-应用数学

CiteScore

4.90

自引率

6.90%

发文量

798

审稿时长

6 months

期刊介绍： Mathematical Methods in the Applied Sciences publishes papers dealing with new mathematical methods for the consideration of linear and non-linear, direct and inverse problems for physical relevant processes over time- and space- varying media under certain initial, boundary, transition conditions etc. Papers dealing with biomathematical content, population dynamics and network problems are most welcome. Mathematical Methods in the Applied Sciences is an interdisciplinary journal: therefore, all manuscripts must be written to be accessible to a broad scientific but mathematically advanced audience. All papers must contain carefully written introduction and conclusion sections, which should include a clear exposition of the underlying scientific problem, a summary of the mathematical results and the tools used in deriving the results. Furthermore, the scientific importance of the manuscript and its conclusions should be made clear. Papers dealing with numerical processes or which contain only the application of well established methods will not be accepted. Because of the broad scope of the journal, authors should minimize the use of technical jargon from their subfield in order to increase the accessibility of their paper and appeal to a wider readership. If technical terms are necessary, authors should define them clearly so that the main ideas are understandable also to readers not working in the same subfield.