Convergence of a stochastic particle approximation for fractional scalar conservation laws

Benjamin Jourdain (1) , Raphaël Roux (1)

1 CERMICS - Centre d'Enseignement et de Recherche en Mathématiques, Informatique et Calcul Scientifique

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.

Keywords: nonlinear partial differential equation; interacting particle system; Euler scheme; alpha-stable Lévy process

Domains: Probability [math.PR]; Analysis of PDEs [math.AP]

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⟩