On the Support of a hypoelliptic diffusion on the Heisenberg group

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.

arXiv commentMajor revision including new introduction and title. arXiv admin note: text overlap with arXiv:1908.09182