Rate of convergence for particle approximation of PDEs in Wasserstein space

Maximilien Germain, Huyên Pham, Xavier Warin

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 for the pathwise error on the solution v and of order for the -error on its L-derivative . The proof relies on backward stochastic differential equation techniques.