An integral equation for Root's barrier and the generation of Brownian increments

Paul Gassiat; Aleksandar Mijatovic; Harald Oberhauser

doi:10.1214/14-AAP1042

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An integral equation for Root's barrier and the generation of Brownian increments

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Paul Gassiat, Aleksandar Mijatovic, Harald Oberhauser

Original language	English
Pages (from-to)	2039-2065
Number of pages	27
Journal	The Annals of Applied Probability
Volume	25
Issue number	4
Early online date	21 May 2015
DOIs	https://doi.org/10.1214/14-AAP1042
E-pub ahead of print	21 May 2015
Published	Aug 2015

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Aleksandar Mijatovic (Mathematics)

Abstract

We derive a nonlinear integral equation to calculate Root’s solution of the Skorokhod embedding problem for atom-free target measures. We then use this to efficiently generate bounded time–space increments of Brownian motion and give a parabolic version of Muller’s classic “Random walk over spheres” algorithm.

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