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.

Stochastic nonlinear Fokker–Planck equations / Coghi, M.; Gess, B.. - In: NONLINEAR ANALYSIS. - ISSN 0362-546X. - 187:(2019), pp. 259-278. [10.1016/j.na.2019.05.003]

Stochastic nonlinear Fokker–Planck equations

Coghi M.;
2019

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.
Coghi, M.; Gess, B.
Stochastic nonlinear Fokker–Planck equations / Coghi, M.; Gess, B.. - In: NONLINEAR ANALYSIS. - ISSN 0362-546X. - 187:(2019), pp. 259-278. [10.1016/j.na.2019.05.003]
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11572/320295
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