HAL : inria-00348693, version 1

DOI : 10.1002/pamm.200700564

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ICIAM 2007, 6th International Congress on Industrial and Applied Mathematics, Zurich : Suisse (2007)

Simulation of exit times and positions for Brownian motions and Diffusions

Madalina Deaconu 1, 2, Antoine Lejay 1, 2

(2007)

We present in this note some variations of the Monte Carlo method for the random walk on spheres which allow to solve many elliptic and parabolic problems involving the Laplace operator or second-order differential operators. In these methods, the spheres are replaced by rectangles or parallelepipeds. Our first method constructs the exit time and the exit position of a rectangle for a Brownian motion. The second method exhibits a variance reduction technique. The main point is to reduce the problem only to the use of some distributions related to the standard one-dimensional Brownian motion.

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

Domaine

:

Mathématiques/Probabilités

Mots-clés : Stochastic Differential Equations – Monte Carlo methods – Random walk on squares – Random walk on rectangles – Variance reduction – Simulation of rare events – Dirichlet/Neumann problems

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Contributeur : Antoine Lejay <>

Soumis le : Samedi 20 Décembre 2008, 02:15:39

Dernière modification le : Samedi 20 Décembre 2008, 09:02:40