Rate of convergence for particle approximation of PDEs in Wasserstein space

Maximilien Germain, Huy\^en Pham and Xavier Warin
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Maximilien Germain: EDF, LPSM, EDF R&D
Huy\^en Pham: LPSM, FiME Lab
Xavier Warin: EDF, FiME Lab, EDF R&D

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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, 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.

Date: 2021-03, Revised 2021-11
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Citations: View citations in EconPapers (1)

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