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Rate of convergence for particle approximation of PDEs in Wasserstein space

Published online by Cambridge University Press:  28 July 2022

Maximilien Germain*
EDF R&D, LPSM, and Université Paris Cité
Huyên Pham*
LPSM, Université Paris Cité, FiME, and CREST ENSAE
Xavier Warin*
EDF R&D, and FiME
*Email address:
**Email address:
***Email address:


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.

Original Article
© The Author(s), 2022. Published by Cambridge University Press on behalf of Applied Probability Trust

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