Stochastic nonlinear Fokker–Planck equations

Stochastic nonlinear Fokker–Planck equations

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...

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Veröffentlicht in:Nonlinear analysis 2019-10, Vol.187, p.259-278
Hauptverfasser: Coghi, Michele, Gess, Benjamin
Format: Artikel
Sprache:eng
Schlagworte:
Mathematical analysis
McKean–Vlasov equations
Nonlinear equations
Particle representations
Stochastic Fokker–Planck equations
Uniqueness
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Zusammenfassung: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.
ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2019.05.003