{"title":"Vitali variation error bounds for expected value functions","authors":"Alban Kryeziu, Ward Romeijnders, Evrim Ursavas","doi":"10.1016/j.orl.2024.107157","DOIUrl":null,"url":null,"abstract":"<div><p>We derive error bounds for two-dimensional expected value functions that depend on the Vitali variation of the joint probability density function of the corresponding random vector. Contrary to bounds from the literature, our bounds are not restricted to underlying functions that are one-dimensional and periodic. In our proof, we first derive the bounds in a discrete setting, which requires us to characterize the extreme points of the set of all matrices that have zero-sum rows and columns and have an <span><math><msub><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span>-norm bounded by one. This result may be of independent interest.</p></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"56 ","pages":"Article 107157"},"PeriodicalIF":0.8000,"publicationDate":"2024-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0167637724000932/pdfft?md5=5492f99c475f8d0118ba920e1fac4d6d&pid=1-s2.0-S0167637724000932-main.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Operations Research Letters","FirstCategoryId":"91","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0167637724000932","RegionNum":4,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"OPERATIONS RESEARCH & MANAGEMENT SCIENCE","Score":null,"Total":0}
引用次数: 0
Abstract
We derive error bounds for two-dimensional expected value functions that depend on the Vitali variation of the joint probability density function of the corresponding random vector. Contrary to bounds from the literature, our bounds are not restricted to underlying functions that are one-dimensional and periodic. In our proof, we first derive the bounds in a discrete setting, which requires us to characterize the extreme points of the set of all matrices that have zero-sum rows and columns and have an -norm bounded by one. This result may be of independent interest.
期刊介绍：
Operations Research Letters is committed to the rapid review and fast publication of short articles on all aspects of operations research and analytics. Apart from a limitation to eight journal pages, quality, originality, relevance and clarity are the only criteria for selecting the papers to be published. ORL covers the broad field of optimization, stochastic models and game theory. Specific areas of interest include networks, routing, location, queueing, scheduling, inventory, reliability, and financial engineering. We wish to explore interfaces with other fields such as life sciences and health care, artificial intelligence and machine learning, energy distribution, and computational social sciences and humanities. Our traditional strength is in methodology, including theory, modelling, algorithms and computational studies. We also welcome novel applications and concise literature reviews.
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