The Annals of Applied Probability
- Ann. Appl. Probab.
- Volume 5, Number 4 (1995), 875-896.
Discretization Error in Simulation of One-Dimensional Reflecting Brownian Motion
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.
Ann. Appl. Probab., Volume 5, Number 4 (1995), 875-896.
First available in Project Euclid: 19 April 2007
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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. https://projecteuclid.org/euclid.aoap/1177004597