English

A conformal Skorokhod embedding

Probability 2019-05-03 v1

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.

Keywords

Cite

@article{arxiv.1905.00852,
  title  = {A conformal Skorokhod embedding},
  author = {Renan Gross},
  journal= {arXiv preprint arXiv:1905.00852},
  year   = {2019}
}

Comments

11 pages, 2 figures

R2 v1 2026-06-23T08:55:27.379Z