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Volume 8, Issue 4
An Efficient Algorithm to Simulate a Brownian Motion Over Irregular Domains

S. Zein, A. Lejay & M. Deaconu

DOI: 10.4208/cicp.240209.031209a

Commun. Comput. Phys., 8 (2010), pp. 901-916.

Published online: 2010-08

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  • Abstract

In this paper, we present an algorithm to simulate a Brownian motion by coupling two numerical schemes: the Euler scheme with the random walk on the hyper-rectangles. This coupling algorithm has the advantage to be able to compute the exit time and the exit position of a Brownian motion from an irregular bounded domain (with corners at the boundary), and being of order one with respect to the time step of the Euler scheme. The efficiency of the algorithm is studied through some numerical examples by comparing the analytical solution with the Monte Carlo solution of some Poisson problems. The Monte Carlo solution of these PDEs requires simulating Brownian motions of different types (natural, reflected or drifted) over an irregular domain.

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@Article{CiCP-8-901, author = {S. Zein, A. Lejay and M. Deaconu}, title = {An Efficient Algorithm to Simulate a Brownian Motion Over Irregular Domains}, journal = {Communications in Computational Physics}, year = {2010}, volume = {8}, number = {4}, pages = {901--916}, abstract = {

In this paper, we present an algorithm to simulate a Brownian motion by coupling two numerical schemes: the Euler scheme with the random walk on the hyper-rectangles. This coupling algorithm has the advantage to be able to compute the exit time and the exit position of a Brownian motion from an irregular bounded domain (with corners at the boundary), and being of order one with respect to the time step of the Euler scheme. The efficiency of the algorithm is studied through some numerical examples by comparing the analytical solution with the Monte Carlo solution of some Poisson problems. The Monte Carlo solution of these PDEs requires simulating Brownian motions of different types (natural, reflected or drifted) over an irregular domain.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.240209.031209a}, url = {http://global-sci.org/intro/article_detail/cicp/7601.html} }
TY - JOUR T1 - An Efficient Algorithm to Simulate a Brownian Motion Over Irregular Domains AU - S. Zein, A. Lejay & M. Deaconu JO - Communications in Computational Physics VL - 4 SP - 901 EP - 916 PY - 2010 DA - 2010/08 SN - 8 DO - http://doi.org/10.4208/cicp.240209.031209a UR - https://global-sci.org/intro/article_detail/cicp/7601.html KW - AB -

In this paper, we present an algorithm to simulate a Brownian motion by coupling two numerical schemes: the Euler scheme with the random walk on the hyper-rectangles. This coupling algorithm has the advantage to be able to compute the exit time and the exit position of a Brownian motion from an irregular bounded domain (with corners at the boundary), and being of order one with respect to the time step of the Euler scheme. The efficiency of the algorithm is studied through some numerical examples by comparing the analytical solution with the Monte Carlo solution of some Poisson problems. The Monte Carlo solution of these PDEs requires simulating Brownian motions of different types (natural, reflected or drifted) over an irregular domain.

S. Zein, A. Lejay and M. Deaconu. (2010). An Efficient Algorithm to Simulate a Brownian Motion Over Irregular Domains. Communications in Computational Physics. 8 (4). 901-916. doi:10.4208/cicp.240209.031209a
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