Abstract
We study the stochastic processes that are images of Brownian motions on Heisenberg group H 2n+1 under conformal maps. In particular, we obtain that Cayley transform maps Brownian paths in H 2n+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 H 2n+1 started from x ≠ 0, is up to time change, a Brownian bridge on H 2n+1 conditioned to be at the origin.
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Wang, J. (2017). Conformal Transforms and Doob’s h-Processes on Heisenberg Groups. In: Baudoin, F., Peterson, J. (eds) Stochastic Analysis and Related Topics. Progress in Probability, vol 72. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-59671-6_8
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DOI: https://doi.org/10.1007/978-3-319-59671-6_8
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