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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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.

Article information

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

Dates
First available: 19 April 2007

Permanent link to this document
http://projecteuclid.org/euclid.aoap/1177004597

JSTOR
links.jstor.org

Digital Object Identifier
doi:10.1214/aoap/1177004597

Mathematical Reviews number (MathSciNet)
MR1384357

Zentralblatt MATH identifier
0853.65147

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

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

Citation

Asmussen, Soren; Glynn, Peter; Pitman, Jim. Discretization Error in Simulation of One-Dimensional Reflecting Brownian Motion. The Annals of Applied Probability 5 (1995), no. 4, 875--896. doi:10.1214/aoap/1177004597. http://projecteuclid.org/euclid.aoap/1177004597.


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