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

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

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

Keywords

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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