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Institut de recherche en informatique et systèmes aléatoires |  |
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Institut de recherche en informatique et systèmes aléatoires | |
| HAL : hal-00649170, version 2 |
| Voir la fiche détaillée |  BibTeX,EndNote,... |
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| Versions disponibles | v1 (07-12-2011) | v2 (21-05-2012) | v3 (20-08-2012) |
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| Simulating diffusion processes in discontinuous media: a numerical scheme with constant time steps |
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| Antoine Lejay 1, 2Géraldine Pichot 3 |
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| TOSCA ; SAGE Collaboration(s) |
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| (02/12/2011) |
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| 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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| 1 : | Institut Elie Cartan Nancy (IECN) |
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CNRS : UMR7502 – INRIA – Université Henri Poincaré - Nancy I – Université Nancy II – Institut National Polytechnique de Lorraine (INPL) |
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| 2 : | TOSCA (INRIA Sophia Antipolis / INRIA Lorraine / IECN) |
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INRIA – CNRS : UMR7502 – Université Henri Poincaré - Nancy I – Université Nancy II – Institut National Polytechnique de Lorraine (INPL) |
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| 3 : | SAGE (INRIA - IRISA) |
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CNRS : UMR6074 – INRIA – Université de Rennes 1 |
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| Probabilités et statistiques |
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| Domaine | : | Mathématiques/Probabilités Physique/Physique/Géophysique Planète et Univers/Sciences de la Terre/Géophysique Sciences de l'environnement/Milieux et Changements globaux |
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| divergence form operators – stochastic differential equation – skew Brownian motion – Monte Carlo simulation – Euler scheme – geophysics – diffusive media with interfaces |
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| Liste des fichiers attachés à ce document : | |||||
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| hal-00649170, version 2 | |
| http://hal.inria.fr/hal-00649170 | |
| oai:hal.inria.fr:hal-00649170 | |
| Contributeur : Antoine Lejay | |
| Soumis le : Lundi 21 Mai 2012, 14:55:12 | |
| Dernière modification le : Jeudi 31 Mai 2012, 14:55:33 | |
