反射随机漫步的无界加法函数的样本路径大偏差

IF 1.4 3区数学 Q2 MATHEMATICS, APPLIED

Mathematics of Operations Research Pub Date : 2024-03-27 DOI:10.1287/moor.2020.0094

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

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引用次数: 0

摘要

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。

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

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].

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来源期刊

Mathematics of Operations Research 管理科学-应用数学

CiteScore

3.40

自引率

5.90%

发文量

178

审稿时长

15.0 months

期刊介绍： Mathematics of Operations Research is an international journal of the Institute for Operations Research and the Management Sciences (INFORMS). The journal invites articles concerned with the mathematical and computational foundations in the areas of continuous, discrete, and stochastic optimization; mathematical programming; dynamic programming; stochastic processes; stochastic models; simulation methodology; control and adaptation; networks; game theory; and decision theory. Also sought are contributions to learning theory and machine learning that have special relevance to decision making, operations research, and management science. The emphasis is on originality, quality, and importance; correctness alone is not sufficient. Significant developments in operations research and management science not having substantial mathematical interest should be directed to other journals such as Management Science or Operations Research.