# Rate of convergence for particle approximation of PDEs in Wasserstein space

arXiv: https://arxiv.org/abs/2103.00837 · HTML: https://mlsanity.com/paper/2103.00837/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Mar 2021.

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

- [Deep Backward and Galerkin Methods for the Finite State Master Equation](https://mlsanity.com/paper/2403.04975/) (2024)
- [Stochastic Control Methods for Optimization](https://mlsanity.com/paper/2601.01248/) (2026)
- [Convergence analysis of controlled particle systems arising in deep learning: from finite to infinite sample size](https://mlsanity.com/paper/2404.05185/) (2024)

## Abstract (arXiv)

We prove a rate of convergence for the N-particle approximation of a second-order partial differential equation in the space of probability measures, like the Master equation or Bellman equation of mean-field control problem under common noise. The rate is of order 1/N for the pathwise error on the solution v and of order 1/√N for the L2-error on its L-derivative partialμ v. The proof relies on backward stochastic differential equations techniques.