Conformal Transforms and Doob’s h-Processes on Heisenberg Groups

  • Jing Wang
Conference paper
Part of the Progress in Probability book series (PRPR, volume 72)


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 \(\mathbb{S}^{2n+1}\) 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.


Brownian bridge Cayley transform Doob’s h-process Heisenberg group Kelvin transform 


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of Illinois at Urbana ChampaignUrbanaUSA

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