Sample-Path Large Deviations for Unbounded Additive Functionals of the Reflected Random Walk

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-03-27 DOI:10.1287/moor.2020.0094

Mihail Bazhba, Jose Blanchet, Chang-Han Rhee, Bert Zwart

引用次数: 0

Abstract

We prove a sample-path large deviation principle (LDP) with sublinear speed for unbounded functionals of certain Markov chains induced by the Lindley recursion. The LDP holds in the Skorokhod space [Formula: see text] equipped with the [Formula: see text] topology. Our technique hinges on a suitable decomposition of the Markov chain in terms of regeneration cycles. Each regeneration cycle denotes the area accumulated during the busy period of the reflected random walk. We prove a large deviation principle for the area under the busy period of the Markov random walk, and we show that it exhibits a heavy-tailed behavior.Funding: The research of B. Zwart and M. Bazhba is supported by the Nederlandse Organisatie voor Wetenschappelijk Onderzoek [Grant 639.033.413]. The research of J. Blanchet is supported by the National Science Foundation (NSF) [Grants 1915967, 1820942, and 1838576] as well as the Defense Advanced Research Projects Agency [Grant N660011824028]. The research of C.-H. Rhee is supported by the NSF [Grant CMMI-2146530].

查看原文本刊更多论文

反射随机漫步的无界加法函数的样本路径大偏差

我们以亚线性速度证明了林德利递推诱导的某些马尔可夫链的无界函数的样本路径大偏差原理（LDP）。大偏差原理在配有[公式：见正文]拓扑的斯科罗霍德空间[公式：见正文]中成立。我们的技术取决于用再生周期对马尔可夫链进行适当的分解。每个再生周期表示在反射随机游走的繁忙期积累的面积。我们证明了马尔可夫随机游走忙周期下面积的大偏差原理，并证明它表现出重尾行为：B. Zwart 和 M. Bazhba 的研究得到了 Nederlandse Organisatie voor Wetenschappelijk Onderzoek [Grant 639.033.413] 的支持。J. Blanchet 的研究得到了美国国家科学基金会（NSF）[1915967、1820942 和 1838576 号资助]以及美国国防部高级研究计划局[N660011824028 号资助]的支持。C.-H.Rhee 的研究得到了美国国家科学基金会 [CMMI-2146530] 的资助。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

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.