The Annals of Applied Probability

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

Paul Gassiat, Aleksandar Mijatović, and Harald Oberhauser

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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.

Article information

Ann. Appl. Probab., Volume 25, Number 4 (2015), 2039-2065.

Received: October 2013
Revised: April 2014
First available in Project Euclid: 21 May 2015

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Zentralblatt MATH identifier

Primary: 60G40: Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60] 45Gxx: Nonlinear integral equations [See also 47H30, 47Jxx] 65C05: Monte Carlo methods
Secondary: 65C40: Computational Markov chains 65C30: Stochastic differential and integral equations

Skorokhod embedding problem Root solution simulation of Brownian motion integral equations for free boundaries


Gassiat, Paul; Mijatović, Aleksandar; Oberhauser, Harald. An integral equation for Root’s barrier and the generation of Brownian increments. Ann. Appl. Probab. 25 (2015), no. 4, 2039--2065. doi:10.1214/14-AAP1042.

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