{"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":49244,"journal":{"name":"Alea-Latin American Journal of Probability and Mathematical Statistics","volume":" ","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2021-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Alea-Latin American Journal of Probability and Mathematical Statistics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.30757/alea.v20-26","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"STATISTICS & PROBABILITY","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.
期刊介绍:
ALEA publishes research articles in probability theory, stochastic processes, mathematical statistics, and their applications. It publishes also review articles of subjects which developed considerably in recent years. All articles submitted go through a rigorous refereeing process by peers and are published immediately after accepted.
ALEA is an electronic journal of the Latin-american probability and statistical community which provides open access to all of its content and uses only free programs. Authors are allowed to deposit their published article into their institutional repository, freely and with no embargo, as long as they acknowledge the source of the paper.
ALEA is affiliated with the Institute of Mathematical Statistics.