1 results
Rate of convergence for particle approximation of PDEs in Wasserstein space
- Part of
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- Journal:
- Journal of Applied Probability / Volume 59 / Issue 4 / December 2022
- Published online by Cambridge University Press:
- 28 July 2022, pp. 992-1008
- Print publication:
- December 2022
-
- Article
- Export citation
-
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.
