Photo by portablepeopleproductions from unsplash
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… Click to show full 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.
Journal Title: Journal of Mathematical Analysis and Applications
Year Published: 2019
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!