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2020 Remarks on Gross’ technique for obtaining a conformal Skorohod embedding of planar Brownian motion
Maher Boudabra, Greg Markowsky
Electron. Commun. Probab. 25: 1-13 (2020). DOI: 10.1214/20-ECP300

Abstract

In [7] it was proved that, given a distribution $\mu $ with zero mean and finite second moment, there exists a simply connected domain $\Omega $ such that if $Z_{t}$ is a standard planar Brownian motion, then $\mathcal{R} e(Z_{\tau _{\Omega }})$ has the distribution $\mu $, where $\tau _{\Omega }$ denotes the exit time of $Z_{t}$ from $\Omega $. In this note, we extend this method to prove that if $\mu $ has a finite $p$-th moment then the first exit time $\tau _{\Omega }$ from $\Omega $ has a finite moment of order $\frac{p} {2}$. We also prove a uniqueness principle for this construction, and use it to give several examples.

Citation

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Maher Boudabra. Greg Markowsky. "Remarks on Gross’ technique for obtaining a conformal Skorohod embedding of planar Brownian motion." Electron. Commun. Probab. 25 1 - 13, 2020. https://doi.org/10.1214/20-ECP300

Information

Received: 27 November 2019; Accepted: 24 February 2020; Published: 2020
First available in Project Euclid: 29 February 2020

zbMATH: 1434.60224
MathSciNet: MR4089727
Digital Object Identifier: 10.1214/20-ECP300

Subjects:
Primary: 30C20, 60J65

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