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Discretization Error in Simulation of One-Dimensional Reflecting Brownian Motion

Soren Asmussen, Peter Glynn and Jim Pitman
The Annals of Applied Probability
Vol. 5, No. 4 (Nov., 1995), pp. 875-896
Stable URL: http://www.jstor.org/stable/2245096
Page Count: 22
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Discretization Error in Simulation of One-Dimensional Reflecting Brownian Motion
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Abstract

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.

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