Consistency of randomized integration methods

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-06-01 DOI:10.1016/j.jco.2023.101740

Julian Hofstadler, Daniel Rudolf

引用次数: 4

Abstract

We prove that a class of randomized integration methods, including averages based on $(t, d)$ -sequences, Latin hypercube sampling, Frolov points as well as Cranley-Patterson rotations, consistently estimates expectations of integrable functions. Consistency here refers to convergence in mean and/or convergence in probability of the estimator to the integral of interest. Moreover, we suggest median modified methods and show for integrands in $L^{p}$ with $p > 1$ consistency in terms of almost sure convergence.

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随机积分方法的一致性

我们证明了一类随机积分方法，包括基于(t,d)序列的平均值，拉丁超立方采样，Frolov点以及Cranley-Patterson旋转，一致地估计了可积函数的期望。这里的一致性指的是对感兴趣的积分的估计量的均值收敛和/或概率收敛。此外，我们提出了中值修正方法，并证明了Lp中具有p>1一致性的被积函数的几乎肯定收敛性。

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

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.