Conformal transforms and Doob's h-processes on Heisenberg groups
Probability
2016-10-03 v1
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 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\not= 0, is up to time change, a Brownian bridge on H2n+1 conditioned to be at the origin.
Keywords
Cite
@article{arxiv.1609.09851,
title = {Conformal transforms and Doob's h-processes on Heisenberg groups},
author = {Jing Wang},
journal= {arXiv preprint arXiv:1609.09851},
year = {2016}
}