# Remarks on gross’ technique for obtaining a conformal skorohod embedding of planar brownian motion

Maher Boudabra, Greg Markowsky

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2 Citations (Scopus)

### Abstract

In [7] 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(Z) 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.

Original language English 20 13 Electronic Communications in Probability 25 https://doi.org/10.1214/20-ECP300 Published - 1 Jan 2020

### Keywords

• Conformal invariance
• Planar Brownian motion