Abstract
AbstractWe 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.
Publisher
Cambridge University Press (CUP)
Subject
Statistics, Probability and Uncertainty,General Mathematics,Statistics and Probability
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