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 Oelschläger [16], [17]. 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.
Uniform convergence of proliferating particles to the FKPP equation
Flandoli F.;
2019
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 Oelschläger [16], [17]. 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.File in questo prodotto:
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