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

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, 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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https://hal.archives-ouvertes.fr/hal-03154021
Contributor : Maximilien Germain Connect in order to contact the contributor
Submitted on : Tuesday, November 16, 2021 - 12:50:17 PM
Last modification on : Monday, January 17, 2022 - 10:44:55 AM

Identifiers

  • HAL Id : hal-03154021, version 3
  • ARXIV : 2103.00837

Citation

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

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