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Rate of convergence for particle approximation of PDEs in Wasserstein space
Published online by Cambridge University Press: 28 July 2022
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 $1/N$ 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.
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- © The Author(s), 2022. Published by Cambridge University Press on behalf of Applied Probability Trust
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