Stochastic theta methods for random periodic solution of stochastic differential equations under non-globally Lipschitz conditions

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY Accounts of Chemical Research Pub Date : 2024-08-05 DOI:10.1007/s11075-024-01892-y

Ziheng Chen, Liangmin Cao, Lin Chen

引用次数: 0

Abstract

This work focuses on the numerical approximations of random periodic solutions of stochastic differential equations (SDEs). Under non-globally Lipschitz conditions, we prove the existence and uniqueness of random periodic solutions for the considered equations and its numerical approximations generated by the stochastic theta (ST) methods with \(\theta \in (1/2,1]\). It is shown that the random periodic solution of each ST method converges strongly in the mean square sense to that of SDEs. More precisely, the mean square convergence order is 1/2 for SDEs with multiplicative noise and 1 for SDEs with additive noise, respectively. Numerical results are finally reported to confirm these theoretical findings.

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非全局 Lipschitz 条件下随机微分方程随机周期解的随机 Theta 方法

这项研究的重点是随机微分方程（SDE）的随机周期解的数值近似。在非全局 Lipschitz 条件下，我们证明了所考虑方程的随机周期解的存在性和唯一性，以及由 \theta \in (1/2,1]\) 随机θ（ST）方法产生的随机周期解的数值近似。结果表明，每种 ST 方法的随机周期解在均方意义上都强烈收敛于 SDE 的随机周期解。更准确地说，对于乘性噪声的 SDE 和加性噪声的 SDE，其均方收敛阶数分别为 1/2 和 1。最后报告的数值结果证实了这些理论发现。

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.

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