In  it was proved that, given a distribution µ with zero mean and finite second moment, there exists a simply connected domain Ω such that if Zt is a standard planar Brownian motion, then Re(ZTΩ) has the distributionµ, where T Ω denotes the exit time of Zt from Ω. In this note, we extend this method to prove that if µ has a finite p-th moment then the first exit time TΩ from Ω has a finite moment of order. We also prove a uniqueness principle for this construction, and use it to give several examples.
- Conformal invariance
- Planar Brownian motion