{"title":"关于Heisenberg群上的次椭圆扩散的支持","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":"{\"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}","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}
On the support of a hypoelliptic diffusion on the Heisenberg group
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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