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Article Dans Une Revue Journal of Applied Probability Année : 2022

Rate of convergence for particle approximation of PDEs in Wasserstein space *

Résumé

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.
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Dates et versions

hal-03154021 , version 1 (26-02-2021)
hal-03154021 , version 2 (24-06-2021)
hal-03154021 , version 3 (16-11-2021)

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Maximilien Germain, Huyên Pham, Xavier Warin. Rate of convergence for particle approximation of PDEs in Wasserstein space *. Journal of Applied Probability, In press, 59 (4). ⟨hal-03154021v3⟩
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