{"title":"基于正则结构的Sobolev粗糙路径扩展定理","authors":"Chong Liu, David J. Promel, J. Teichmann","doi":"10.1051/ps/2022016","DOIUrl":null,"url":null,"abstract":"We show that every $\\R^d$-valued Sobolev path with regularity~$\\alpha$ and integrability~$p$ can be lifted to a Sobolev rough path provided $1/2 >\\alpha > 1/p \\vee 1/3$. The novelty of our approach is its use of ideas underlying Hairer's reconstruction theorem generalized to a framework allowing for Sobolev models and Sobolev modelled distributions. Moreover, we show that the corresponding lifting map is locally Lipschitz continuous with respect to the inhomogeneous Sobolev metric.","PeriodicalId":51249,"journal":{"name":"Esaim-Probability and Statistics","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2021-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"A Sobolev rough path extension theorem via regularity structures\",\"authors\":\"Chong Liu, David J. Promel, J. Teichmann\",\"doi\":\"10.1051/ps/2022016\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We show that every $\\\\R^d$-valued Sobolev path with regularity~$\\\\alpha$ and integrability~$p$ can be lifted to a Sobolev rough path provided $1/2 >\\\\alpha > 1/p \\\\vee 1/3$. The novelty of our approach is its use of ideas underlying Hairer's reconstruction theorem generalized to a framework allowing for Sobolev models and Sobolev modelled distributions. Moreover, we show that the corresponding lifting map is locally Lipschitz continuous with respect to the inhomogeneous Sobolev metric.\",\"PeriodicalId\":51249,\"journal\":{\"name\":\"Esaim-Probability and Statistics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2021-04-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Esaim-Probability and Statistics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1051/ps/2022016\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"STATISTICS & PROBABILITY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Esaim-Probability and Statistics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1051/ps/2022016","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
A Sobolev rough path extension theorem via regularity structures
We show that every $\R^d$-valued Sobolev path with regularity~$\alpha$ and integrability~$p$ can be lifted to a Sobolev rough path provided $1/2 >\alpha > 1/p \vee 1/3$. The novelty of our approach is its use of ideas underlying Hairer's reconstruction theorem generalized to a framework allowing for Sobolev models and Sobolev modelled distributions. Moreover, we show that the corresponding lifting map is locally Lipschitz continuous with respect to the inhomogeneous Sobolev metric.
期刊介绍:
The journal publishes original research and survey papers in the area of Probability and Statistics. It covers theoretical and practical aspects, in any field of these domains.
Of particular interest are methodological developments with application in other scientific areas, for example Biology and Genetics, Information Theory, Finance, Bioinformatics, Random structures and Random graphs, Econometrics, Physics.
Long papers are very welcome.
Indeed, we intend to develop the journal in the direction of applications and to open it to various fields where random mathematical modelling is important. In particular we will call (survey) papers in these areas, in order to make the random community aware of important problems of both theoretical and practical interest. We all know that many recent fascinating developments in Probability and Statistics are coming from "the outside" and we think that ESAIM: P&S should be a good entry point for such exchanges. Of course this does not mean that the journal will be only devoted to practical aspects.