An Efficient Algorithm to Simulate a Brownian Motion Over Irregular Domains

Samih Zein 1, 2 Antoine Lejay 1, 2 Madalina Deaconu 1, 2
2 TOSCA
INRIA Lorraine, CRISAM - Inria Sophia Antipolis - Méditerranée , UHP - Université Henri Poincaré - Nancy 1, Université Nancy 2, INPL - Institut National Polytechnique de Lorraine, CNRS - Centre National de la Recherche Scientifique : UMR7502
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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Communications in Computational Physics, Global Science Press, 2010, 8 (4), pp.901-916. <10.4208/cicp.240209.031209a>
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Samih Zein, Antoine Lejay, Madalina Deaconu. An Efficient Algorithm to Simulate a Brownian Motion Over Irregular Domains. Communications in Computational Physics, Global Science Press, 2010, 8 (4), pp.901-916. <10.4208/cicp.240209.031209a>. <inria-00444056>

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