Convergence of a stochastic particle approximation for fractional scalar conservation laws

Details Convergence of a stochastic particle approximation for fractional scalar conservation laws Convergence of a stochastic particle approximation for fractional scalar conservation laws

2010-06-21

arxiv.org/abs/1006.4047v1

Mathematics

Probability

Scientific paper

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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