Stein’s method, Gaussian processes and Palm measures, with applications to queueing

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-10-01 DOI:10.1214/22-aap1908

A. D. Barbour, Nathan Ross, Guangqu Zheng

引用次数: 2

Abstract

We develop a general approach to Stein’s method for approximating a random process in the path space D([0,T]→Rd) by a real continuous Gaussian process. We then use the approach in the context of processes that have a representation as integrals with respect to an underlying point process, deriving a general quantitative Gaussian approximation. The error bound is expressed in terms of couplings of the original process to processes generated from the reduced Palm measures associated with the point process. As applications, we study certain GI/GI/∞ queues in the “heavy traffic” regime.

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斯坦的方法，高斯过程和棕榈测量，与应用排队

本文提出了用真实连续高斯过程逼近路径空间D([0,T]→Rd)中的随机过程的一般方法。然后，我们将该方法用于具有相对于底层点过程的积分表示的过程的上下文中，推导出一般定量的高斯近似。误差界限用原始过程与由与点过程相关的简化Palm度量生成的过程的耦合来表示。作为应用，我们研究了“大流量”环境下的GI/GI/∞队列。

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.