Convergence of a stochastic particle approximation for fractional scalar conservation laws

Benjamin Jourdain and Raphaël Roux

Stochastic Processes and their Applications, 2011, vol. 121, issue 5, 957-988

Abstract: We are interested in a probabilistic approximation of the solution to scalar conservation laws with fractional diffusion and nonlinear drift. The probabilistic interpretation of this equation is based on a stochastic differential equation driven by an [alpha]-stable Lévy process and involving a nonlinear drift. The approximation is constructed using a system of particles following a time-discretized version of this stochastic differential equation, with nonlinearity replaced by interaction. We prove convergence of the particle approximation to the solution of the conservation law as the number of particles tends to infinity whereas the discretization step tends to 0 in some precise asymptotics.

Keywords: Nonlinear; partial; differential; equations; Interacting; particle; systems; Euler; scheme; [alpha]-stable; Lévy; processes (search for similar items in EconPapers)
Date: 2011
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Citations: View citations in EconPapers (2)

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