HAL : inria-00444056, version 1

DOI : 10.4208/cicp.240209.031209a

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Communications in Computational Physics 8, 4 (2010) 901-916

An Efficient Algorithm to Simulate a Brownian Motion Over Irregular Domains

Samih Zein 1, 2, Antoine Lejay 1, 2, Madalina Deaconu 1, 2

(01/10/2010)

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.

1 :	Institut Elie Cartan Nancy (IECN)
	CNRS : UMR7502 – INRIA – Université Henri Poincaré - Nancy I – Université Nancy II – Institut National Polytechnique de Lorraine
2 :	TOSCA (INRIA Sophia Antipolis / INRIA Lorraine / IECN)
	INRIA – CNRS : UMR7502 – Université Henri Poincaré - Nancy I – Université Nancy II – Institut National Polytechnique de Lorraine

Équipe de recherche (sauf Inria) : Probabilités et statistique

Domaine

:

Mathématiques/Probabilités

Mots-clés : Brownian Motion – Monte Carlo Methods – Partial Differential Equations – Euler Scheme – Random Walk On Rectangles

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Contributeur : Antoine Lejay <>

Soumis le : Mardi 5 Janvier 2010, 15:40:18

Dernière modification le : Mardi 25 Mai 2010, 14:43:05