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November, 1995 Discretization Error in Simulation of One-Dimensional Reflecting Brownian Motion
Soren Asmussen, Peter Glynn, Jim Pitman
Ann. Appl. Probab. 5(4): 875-896 (November, 1995). DOI: 10.1214/aoap/1177004597


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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Soren Asmussen. Peter Glynn. Jim Pitman. "Discretization Error in Simulation of One-Dimensional Reflecting Brownian Motion." Ann. Appl. Probab. 5 (4) 875 - 896, November, 1995.


Published: November, 1995
First available in Project Euclid: 19 April 2007

zbMATH: 0853.65147
MathSciNet: MR1384357
Digital Object Identifier: 10.1214/aoap/1177004597

Primary: 65C05
Secondary: 60H10 , 60J65

Keywords: Bessel bridge , Bessel process , bias , Euler scheme , excursion , Path decomposition , Riemann zeta function , Spitzer's identity , Stochastic differential equation

Rights: Copyright © 1995 Institute of Mathematical Statistics


Vol.5 • No. 4 • November, 1995
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