Rate of convergence for particle approximation of PDEs in Wasserstein space

Abstract

Abstract We prove a rate of convergence for the N -particle approximation of a second-order partial differential equation in the space of probability measures, such as the master equation or Bellman equation of the 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 $1/\sqrt{N}$ for the $L^2$ -error on its L -derivative $\partial_\mu v$ . The proof relies on backward stochastic differential equation techniques.