Brownian motion and stereographic projection (Q1059335)

Stereographic projection maps \(R^ N\) to \(S^ N\) conformally. For \(N=2\) this map transforms Brownian paths on \(R^ 2\) into Brownian paths on the sphere \(S^ 2\). The paper shows that, for N exceeding 2, stereographic projection transforms Brownian paths on \(R^ N\) into the paths of Brownian motion on \(S^ N\) which is conditioned to be at the pole of the projection at a negative exponential time. The relation of this property to the conformality of the map is also described.