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.;
2019-01-01
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.File in questo prodotto:
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