A scheme for simulating one-dimensional diffusion processes with discontinuous coefficients

Antoine Lejay 1, 2 Miguel Martinez 1
1 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
2 IECN - Institut Élie Cartan de Nancy
Abstract : The aim of this article is to provide a scheme for simulating diffusion processes evolving in one-dimensional discontinuous media. This scheme does not rely on smoothing the coefficients that appear in the infinitesimal generator of the diffusion processes, but uses instead an exact description of the behavior of their trajectories when they reach the points of discontinuity. This description is supplied with the local comparison of the trajectories of the diffusion processes with those of a Skew Brownian Motion.
Keywords : Monte Carlo methods Skew Brownian motion Divergence form operator One-dimensional diffusion Local time Scale function Speed measure
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Journal articles
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Submitted on : Monday, March 20, 2006 - 1:05:11 PM
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Antoine Lejay, Miguel Martinez. A scheme for simulating one-dimensional diffusion processes with discontinuous coefficients. Annals of Applied Probability, Institute of Mathematical Statistics (IMS), 2006, 16 (1), pp.107-139. ⟨10.1214/105051605000000656⟩. ⟨inria-00000410⟩

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