Uniform approximation of FKPP equation by stochastic particle systems

Franco Flandoli, Matti Leimbach, Christian Olivera

Published 2016-04-11Version 1

In this paper we consider a system of Brownian particles with proliferation whose rate depends on the empirical measure. The dependence is more local than a mean field one and has been called moderate interaction by Oelschl\"{a}ger [15], [16]. We prove that the empirical process converges, uniformly in the space variable, to the solution of the Fisher-Kolmogorov-Petrowskii-Piskunov equation. We use a semigroup approach which is new in the framework of these systems.