Discretization Error in Simulation of One-dimensional Reflecting Brownian Motion

S. Asmussen, P. W. Glynn, and J. Pitman

The Annals of Applied Probability,Vol. 5 (4), 875-896 (1995)

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.