# On the system of partial differential equations arising in mean field type control

arXiv: https://arxiv.org/abs/1503.05044 · HTML: https://mlsanity.com/paper/1503.05044/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Mar 2015.

## Built on by (most cited first, 4 of 4)

- [Scaling up Mean Field Games with Online Mirror Descent](https://mlsanity.com/paper/2103.00623/) (2021)
- [Deep Learning for Mean Field Optimal Transport](https://mlsanity.com/paper/2302.14739/) (2023)
- [Learning to Stop: Deep Learning for Mean Field Optimal Stopping](https://mlsanity.com/paper/2410.08850/) (2024)
- [A Constraint-Preserving Neural Network Approach for Solving Mean-Field Games Equilibrium](https://mlsanity.com/paper/2501.17450/) (2025)

## Abstract (arXiv)

We discuss the system of Fokker-Planck and Hamilton-Jacobi-Bellman equations arising from the finite horizon control of McKean-Vlasov dynamics. We give examples of existence and uniqueness results. Finally, we propose some simple models for the motion of pedestrians and report about numerical simulations in which we compare mean filed games and mean field type control.