Abstract
Start a planar Brownian motion and let it run until it hits some given barrier. We show that the barrier may be crafted so that the $x$ coordinate at the hitting time has any prescribed centered distribution with finite variance. This provides a new, complex-analytic proof of the Skorokhod embedding theorem. Our method is constructive and can give an explicit description of the barrier.
Citation
Renan Gross. "A conformal Skorokhod embedding." Electron. Commun. Probab. 24 1 - 11, 2019. https://doi.org/10.1214/19-ECP272
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