Stochastic nonlinear Fokker–Planck equations. (October 2019)

• Record Type: Journal Article
• Authors: Coghi, Michele; Gess, Benjamin
• Is Part Of: Nonlinear analysis. Volume 187(2019)
• Page Start: 259
• Page End: 278
• Publication Date: 2019-10
• Subjects: Stochastic Fokker–Planck equations -- McKean–Vlasov equations -- Particle representations; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2019.05.003
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: The existence and uniqueness of measure-valued solutions to stochastic nonlinear, non-local Fokker–Planck equations is proven. This type of stochastic PDE is shown to arise in the mean field limit of weakly interacting diffusions with common noise. The uniqueness of solutions is obtained without any higher moment assumption on the solution by means of a duality argument to a backward stochastic PDE.