Rate of convergence for particle approximation of PDEs in Wasserstein space

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.