Simulating diffusion processes in discontinuous media: A numerical scheme with constant time steps |
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Authors: | Antoine Lejay Géraldine Pichot |
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Affiliation: | 1. Université de Lorraine, IECN, UMR 7502, Vand?uvre-lés-Nancy, F-54500, France;2. CNRS, IECN, UMR 7502, Vand?uvre-lés-Nancy, F-54500, France;3. Inria, Villers-lés-Nancy, F-54600, France;4. IECN, BP 70238, F-54506 Vand?uvre-lés-Nancy Cedex, France;5. Inria, Rennes - Bretagne Atlantique, Campus de Beaulieu, 35042 Rennes Cedex, France;6. INRIA, Campus de Beaulieu, 35042 Rennes Cedex, France |
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Abstract: | In this article, we propose new Monte Carlo techniques for moving a diffusive particle in a discontinuous media. In this framework, we characterize the stochastic process that governs the positions of the particle. The key tool is the reduction of the process to a Skew Brownian motion (SBM). In a zone where the coefficients are locally constant on each side of the discontinuity, the new position of the particle after a constant time step is sampled from the exact distribution of the SBM process at the considered time. To do so, we propose two different but equivalent algorithms: a two-steps simulation with a stop at the discontinuity and a one-step direct simulation of the SBM dynamic. Some benchmark tests illustrate their effectiveness. |
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