Convergence of a stochastic particle approximation for fractional scalar conservation laws

Benjamin Jourdain; Raphaël Roux

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arXiv · 1006.4047

Convergence of a stochastic particle approximation for fractional scalar conservation laws

Benjamin Jourdain·Raphaël Roux

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Abstract

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 L\'evy 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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Benjamin Jourdain, Raphaël Roux. 2010-06-21. Convergence of a stochastic particle approximation for fractional scalar conservation laws. https://arxiv.org/abs/1006.4047

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