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Article Dans Une Revue Stochastic Processes and their Applications Année : 2011

Convergence of a stochastic particle approximation for fractional scalar conservation laws

Résumé

We give a probabilistic numerical method for solving a partial differential equation with fractional diffusion and nonlinear drift. The probabilistic interpretation of this equation uses a system of particles driven by Lévy alpha-stable processes and interacting with their drift through their empirical cumulative distribution function. We show convergence to the solution for the associated Euler scheme.
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hal-00493773 , version 1 (21-06-2010)

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Benjamin Jourdain, Raphaël Roux. Convergence of a stochastic particle approximation for fractional scalar conservation laws. Stochastic Processes and their Applications, 2011, 121 (5), pp.957-988. ⟨10.1016/j.spa.2011.01.012⟩. ⟨hal-00493773⟩
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