Convergence of a partially truncated Euler-Maruyama method for SDEs with super-linear piecewise continuous drift and Hölder diffusion coefficients

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-09-04 DOI:10.1007/s11075-024-01928-3

Amir Haghighi

引用次数: 0

Abstract

The main purpose of this paper is to develop and analyze a partially truncated Euler-Maruyama method for numerically solving SDEs with super-linear piecewise continuous drift coefficients and \(\varvec{(1/2+\alpha )}\)-Hölder diffusion coefficients (PTEMH), for \(\varvec{\alpha \in [0,1/2]}\). We first present an analytical form for the unique solution of such problems. Then we establish the strong convergence theory of the PTEMH scheme. We show that the convergence rate of the proposed method in the case \(\varvec{\alpha \in (0,1/2]}\) reaches \(\varvec{\alpha }\), which is optimal compared to the explicit Euler-Maruyama method. Finally, numerical results are given to confirm the theoretical convergence rate.

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具有超线性片断连续漂移和霍尔德扩散系数的 SDE 的部分截断欧拉-Maruyama 方法的收敛性

本文的主要目的是开发和分析一种部分截断的 Euler-Maruyama 方法，用于数值求解具有超线性片断连续漂移系数和 \(\varvec{(1/2+\alpha )})-Hölder 扩散系数（PTEMH）的 SDEs，对于 \(\varvec{\alpha \in [0,1/2]}\).我们首先给出了此类问题唯一解的解析形式。然后，我们建立了 PTEMH 方案的强收敛理论。我们表明，在 \(\varvec\{alpha \in (0,1/2]}\) 的情况下，所提出方法的收敛速率达到了 \(\varvec\{alpha }\) ，这与显式 Euler-Maruyama 方法相比是最优的。最后，给出的数值结果证实了理论上的收敛速度。

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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.