# Comparison of viscosity solutions for a class of second order PDEs on the Wasserstein space

arXiv: https://arxiv.org/abs/2309.05040 · HTML: https://mlsanity.com/paper/2309.05040/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Sep 2023.

## Built on by (most cited first, 3 of 3)

- [Policy Gradient for Continuous-Time Mean-Field Control](https://mlsanity.com/paper/2605.20718/) (2026)
- [Mean-Field PhiBE: Continuous-Time Mean-Field Reinforcement Learning from Discrete-Time Data](https://mlsanity.com/paper/2606.26498/) (2026)
- [Reasoning without Regret](https://mlsanity.com/paper/2504.09777/) (2025)

## Abstract (arXiv)

We prove a comparison result for viscosity solutions of second order parabolic partial differential equations in the Wasserstein space. The comparison is valid for semisolutions that are Lipschitz continuous in the measure in a Fourier-Wasserstein metric and uniformly continuous in time. The class of equations we consider is motivated by Mckean-Vlasov control problems with common noise and filtering problems. The proof of comparison relies on a novel version of Ishii's lemma, which is tailor-made for the class of equations we consider.