A conformal Skorokhod embedding

2019/05/02 by Renan Gross, Gross, Renan · 3 citations
Mathematics · #FOS: Mathematics #Probability (math.PR) #math.PR

paper · pdf · doi:10.48550/arxiv.1905.00852

11 pages, 2 figures

arxiv created 2019/05/02 · arxiv updated 2019/05/03

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.

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• A note on the planar Skorokhod embedding problem
• Optimal design for the planar Skorokhod embedding problem
• A Numerical scheme to approximate the solution of the planar Skorokhod embedding problem

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