Uniqueness for solutions of Fokker-Planck equations on infinite dimensional spaces

TL;DR

This paper introduces a new technique to establish the uniqueness of solutions for Fokker-Planck equations in infinite-dimensional spaces, applicable to complex cases with irregular coefficients and degenerate operators.

Contribution

The authors develop a general method for proving uniqueness of solutions to infinite-dimensional Fokker-Planck equations, including challenging cases with irregular coefficients.

Findings

Successfully applied the method to Hilbert space Fokker-Planck equations

Handled equations with irregular coefficients and degenerate operators

Provided a unified approach for uniqueness proofs in infinite dimensions

Abstract

We develop a general technique to prove uniqueness of solutions for Fokker--Planck equations on infinite dimensional spaces. We illustrate this method by implementing it for Fokker--Planck equations in Hilbert spaces with Kolmogorov operators with irregular coefficients and both non-degenerate or degenerate second order part.