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arXiv · 1604.03055

Uniform convergence of proliferating particles to the FKPP equation

Franco Flandoli·Matti Leimbach·Christian Olivera
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Abstract

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 Oelschlager [17], [18]. 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 and is inspired by some literature on stochastic partial differential equations.

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Franco Flandoli, Matti Leimbach, Christian Olivera. 2016-04-11. Uniform convergence of proliferating particles to the FKPP equation. https://arxiv.org/abs/1604.03055

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