Rate of convergence for particles approximation of PDEs in Wasserstein space *

Maximilien Germain (1, 2) , Huyên Pham (3, 4) , Xavier Warin (1, 4)

1 EDF - EDF
2 LPSM (UMR_8001) - Laboratoire de Probabilités, Statistique et Modélisation
3 LPSM (UMR_8001) - Laboratoire de Probabilités, Statistique et Modélisation
4 FiME Lab - Laboratoire de Finance des Marchés d'Energie

We prove a rate of convergence of order 1/N 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 proof relies on backward stochastic differential equations techniques.

Domaines: Finance quantitative [q-fin.CP]; Optimisation et contrôle [math.OC]; Probabilités [math.PR]

Maximilien Germain, Huyên Pham, Xavier Warin. Rate of convergence for particles approximation of PDEs in Wasserstein space *. 2021. ⟨hal-03154021v1⟩