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