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Fabrice Baudoin, Jing Wang (2016)
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- Publisher
- Springer International Publishing
- Copyright
- © Springer International Publishing AG 2017
- ISBN
- 978-3-319-59670-9
- Pages
- 165 –177
- DOI
- 10.1007/978-3-319-59671-6_8
- Publisher site
- See Chapter on Publisher Site
Abstract
[We study the stochastic processes that are images of Brownian motions on Heisenberg group H2n+1 under conformal maps. In particular, we obtain that Cayley transform maps Brownian paths in H2n+1 to a time changed Brownian motion on CR sphere 𝕊2n+1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\mathbb{S}^{2n+1}$$ \end{document} conditioned to be at its south pole at a random time. We also obtain that the inversion of Brownian motion on H2n+1 started from x ≠ 0, is up to time change, a Brownian bridge on H2n+1 conditioned to be at the origin.]
Published: Sep 27, 2017
Keywords: Brownian bridge; Cayley transform; Doob’s h-process; Heisenberg group; Kelvin transform