The Annals of Applied Probability

Discretization Error in Simulation of One-Dimensional Reflecting Brownian Motion

Soren Asmussen, Peter Glynn, and Jim Pitman

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This paper is concerned with various aspects of the simulation of one-dimensional reflected (or regulated) Brownian motion. The main result shows that the discretization error associated with the Euler scheme for simulation of such a process has both a strong and weak order of convergence of precisely 1/2. This contrasts with the faster order 1 achievable for simulations of SDE's without reflecting boundaries. The asymptotic distribution of the discretization error is described using Williams' decomposition of a Brownian path at the time of a minimum. Improved methods for simulation of reflected Brownian motion are discussed.

Article information

Ann. Appl. Probab. Volume 5, Number 4 (1995), 875-896.

First available in Project Euclid: 19 April 2007

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Primary: 65C05: Monte Carlo methods
Secondary: 60J65: Brownian motion [See also 58J65] 60H10: Stochastic ordinary differential equations [See also 34F05]

Bessel bridge Bessel process bias excursion Euler scheme path decomposition Riemann zeta function Spitzer's identity stochastic differential equation


Asmussen, Soren; Glynn, Peter; Pitman, Jim. Discretization Error in Simulation of One-Dimensional Reflecting Brownian Motion. Ann. Appl. Probab. 5 (1995), no. 4, 875--896. doi:10.1214/aoap/1177004597.

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