TY - JOUR
T1 - An Efficient Algorithm to Simulate a Brownian Motion Over Irregular Domains
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 - <p style="text-align: justify;">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.</p>