Rate of convergence for particle approximation of PDEs in Wasserstein space *
Résumé
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 $1/\sqrt{N}$ for the $L^2$-error on its $L$-derivative $\partial_\mu v$.
The proof relies on backward stochastic differential equations techniques.
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