{"title":"Quantitative control of Wasserstein distance between Brownian motion and the Goldstein–Kac telegraph process","authors":"G. Barrera, J. Lukkarinen","doi":"10.1214/22-AIHP1288","DOIUrl":null,"url":null,"abstract":"In this manuscript, we provide a non-asymptotic process level control between the telegraph process and the Brownian motion with suitable diffusivity constant via a Wasserstein distance with quadratic average cost. In addition, we derive non-asymptotic estimates for the corresponding time average $p$-th moments. The proof relies on coupling techniques such as coin-flip coupling, synchronous coupling and the Koml\\'os--Major--Tusn\\'ady coupling.","PeriodicalId":42884,"journal":{"name":"Annales de l Institut Henri Poincare D","volume":"11 1","pages":""},"PeriodicalIF":1.5000,"publicationDate":"2022-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annales de l Institut Henri Poincare D","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1214/22-AIHP1288","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
引用次数: 2
Abstract
In this manuscript, we provide a non-asymptotic process level control between the telegraph process and the Brownian motion with suitable diffusivity constant via a Wasserstein distance with quadratic average cost. In addition, we derive non-asymptotic estimates for the corresponding time average $p$-th moments. The proof relies on coupling techniques such as coin-flip coupling, synchronous coupling and the Koml\'os--Major--Tusn\'ady coupling.