Simulation of diffusions by means of importance sampling paradigm

Madalina Deaconu 1, 2 Antoine Lejay 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 : The aim of this paper is to introduce a new Monte Carlo method based on importance sampling techniques for the simulation of stochastic differential equations. The main idea is here to combine random walk on squares or rectangles methods with importance sampling techniques. The first interest of this approach is that the weights can be easily computed from the density of the one-dimensional Brownian motion. Compared to the Euler scheme this method allows to obtain a more accurate approximation of diffusions when one has to consider complex boundary conditions. The method provides also an interesting alternative to perform variance reduction techniques and to simulate rare events.
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Madalina Deaconu, Antoine Lejay. Simulation of diffusions by means of importance sampling paradigm. Annals of Applied Probability, Institute of Mathematical Statistics (IMS), 2010, 20 (4), pp.1389-1424. ⟨10.1214/09-AAP659⟩. ⟨inria-00126339v2⟩

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