{"title":"Cramér type moderate deviation for random walks conditioned to stay positive","authors":"Mingyang Sun","doi":"10.1016/j.spl.2024.110258","DOIUrl":null,"url":null,"abstract":"<div><p>We establish a Cramér type moderate deviation for random walks conditioned to stay positive, which gives the relative error for the central limit theorem proved by Iglehart (1974). Unlike the traditional technique of conjugate distributions, our approach is based on the strong approximation between random walks and Brownian motion in the same vein as Grama and Xiao (2021).</p></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"216 ","pages":"Article 110258"},"PeriodicalIF":0.9000,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S016771522400227X/pdfft?md5=33bdbf19368db3b1db5c1e8832523f3f&pid=1-s2.0-S016771522400227X-main.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Statistics & Probability Letters","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S016771522400227X","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
引用次数: 0
Abstract
We establish a Cramér type moderate deviation for random walks conditioned to stay positive, which gives the relative error for the central limit theorem proved by Iglehart (1974). Unlike the traditional technique of conjugate distributions, our approach is based on the strong approximation between random walks and Brownian motion in the same vein as Grama and Xiao (2021).
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