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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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