随机微分方程驯服指数积分器的弱收敛性

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-07-11 DOI:10.1007/s10543-024-01029-6

Utku Erdoğan, Gabriel J. Lord

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引用次数: 0

摘要

我们证明了一类基于指数的积分器对具有非全局 Lipschitz 漂移的 SDE 的一阶弱收敛性。我们的分析涵盖了基于几何布朗运动（GBM）方法的驯化版本以及标准指数方案。通过四种不同的多级蒙特卡洛技术，我们对 GBM 和指数驯化方法的数值性能进行了比较。我们发现，与 GBM 驯化法不同，对于线性噪声，标准指数驯化法需要严格限制步长。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Weak convergence of tamed exponential integrators for stochastic differential equations

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Weak convergence of tamed exponential integrators for stochastic differential equations

We prove weak convergence of order one for a class of exponential based integrators for SDEs with non-globally Lipschitz drift. Our analysis covers tamed versions of Geometric Brownian Motion (GBM) based methods as well as the standard exponential schemes. The numerical performance of both the GBM and exponential tamed methods through four different multi-level Monte Carlo techniques are compared. We observe that for linear noise the standard exponential tamed method requires severe restrictions on the step size unlike the GBM tamed method.

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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.