Non-local Conservation Law from Stochastic Particle Systems

Christian Olivera, Marielle Simon

Published 2017-01-17Version 1

In this paper we consider an interacting particle system in $\mathbb{R}^d$ modelled as a system of $N$ stochastic differential equations driven by L\'{e}vy processes. The limiting behaviour as the size $N$ grows to infinity is achieved as a law of large numbers for the empirical density process associated with the interacting particle system. We prove that the empirical process converges, uniformly in the space variable, to the solution of the $d$-dimensional fractal conservation law.