# Stochastic nonlinear Fokker-Planck equations

## TL;DR

This paper proves the existence and uniqueness of measure-valued solutions for stochastic nonlinear non-local Fokker-Planck equations, which model mean field limits of interacting diffusions with common noise, using a duality approach.

## Contribution

It establishes the first rigorous proof of solution existence and uniqueness for this class of stochastic PDEs without requiring higher moment assumptions.

## Key findings

- Existence of measure-valued solutions is proven.
- Uniqueness is established via a duality argument.
- Results apply to mean field limits with common noise.

## 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.