{"title":"Ornstein-Uhlenbeck fluctuations for the line counting process of the ancestral selection graph","authors":"Florin Boenkost, Anna-Lena Weinel","doi":"arxiv-2409.10360","DOIUrl":null,"url":null,"abstract":"For the Moran model with strong or moderately strong selection we prove that\nthe fluctuations around the deterministic limit of the line counting process of\nthe ancestral selection graph converges to an Ornstein-Uhlenbeck process. To\nthis purpose we provide an extension of a functional limit theorem by Ethier\nand Kurtz 1986. This result and a small adaptation of our arguments can also be\nused to obtain the scaling limit for the fluctuations of certain logistic\nbranching processes.","PeriodicalId":501245,"journal":{"name":"arXiv - MATH - Probability","volume":"71 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Probability","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.10360","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
For the Moran model with strong or moderately strong selection we prove that
the fluctuations around the deterministic limit of the line counting process of
the ancestral selection graph converges to an Ornstein-Uhlenbeck process. To
this purpose we provide an extension of a functional limit theorem by Ethier
and Kurtz 1986. This result and a small adaptation of our arguments can also be
used to obtain the scaling limit for the fluctuations of certain logistic
branching processes.