具有不连续漂移的跳跃-扩散 SDE 的误差下限和近似最优性

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-09-09 DOI:10.1007/s10543-024-01036-7

Paweł Przybyłowicz, Verena Schwarz, Michaela Szölgyenyi

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引用次数: 0

摘要

本文证明了具有不连续漂移的跳跃扩散随机微分方程（SDE）数值方法的尖锐误差下限。本文研究了用非自适应和跳变自适应近似方案对跳跃扩散随机微分方程的近似，并为这两类近似方案提供了 3/4 阶的误差下限。由此得出了基于变换的跳变适应准米尔斯坦方案的最优性。

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Lower error bounds and optimality of approximation for jump-diffusion SDEs with discontinuous drift

In this paper sharp lower error bounds for numerical methods for jump-diffusion stochastic differential equations (SDEs) with discontinuous drift are proven. The approximation of jump-diffusion SDEs with non-adaptive as well as jump-adapted approximation schemes is studied and lower error bounds of order 3/4 for both classes of approximation schemes are provided. This yields optimality of the transformation-based jump-adapted quasi-Milstein scheme.

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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.