Simulation of a diffusion process by using the importance sampling paradigm

Madalina Deaconu 1, 2 Antoine Lejay 1, 2
2 OMEGA - Probabilistic numerical methods
CRISAM - Inria Sophia Antipolis - Méditerranée , UHP - Université Henri Poincaré - Nancy 1, Université Nancy 2, CNRS - Centre National de la Recherche Scientifique : UMR7502
Abstract : We construct in this paper a Monte Carlo method in order to approach solutions of multi-dimensional Stochastic Differential Equations processes which relies on the importance sampling technique. Our method is based on the random walk on squares/rectangles method and the main interest of this construction is that the weights are easily computed from the density of the one-dimensional Brownian motion. The advantage we take on the Euler scheme is that this method allows us to get a better simulation of diffusions when one has really to take care of the boundary conditions. Moreover, it provides a good alternative to perform variance reduction techniques and simulation of rare events.
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Submitted on : Wednesday, January 24, 2007 - 5:28:51 PM
Last modification on : Monday, February 18, 2019 - 7:52:04 PM
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  • HAL Id : inria-00126339, version 1


Madalina Deaconu, Antoine Lejay. Simulation of a diffusion process by using the importance sampling paradigm. Annals of Applied Probability, Institute of Mathematical Statistics (IMS), 2007. ⟨inria-00126339v1⟩



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