{"title":"On the support of a hypoelliptic diffusion on the Heisenberg group","authors":"M. Carfagnini","doi":"10.30757/alea.v20-26","DOIUrl":null,"url":null,"abstract":"We provide an elementary proof of the support of the law of a hypoelliptic Brownian motion on the Heisenberg group $\\mathbb{H}$. We consider a control norm associated to left-invariant vector fields on $\\mathbb{H}$, and describe the support in terms of the space of finite energy horizontal curves.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.30757/alea.v20-26","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
We provide an elementary proof of the support of the law of a hypoelliptic Brownian motion on the Heisenberg group $\mathbb{H}$. We consider a control norm associated to left-invariant vector fields on $\mathbb{H}$, and describe the support in terms of the space of finite energy horizontal curves.
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