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Rate of convergence for particle approximation of PDEs in Wasserstein space

Author

Listed:
  • Maximilien Germain

    (EDF, LPSM, EDF R&D)

  • Huy^en Pham

    (LPSM, FiME Lab)

  • Xavier Warin

    (EDF, FiME Lab, EDF R&D)

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.

Suggested Citation

  • Maximilien Germain & Huy^en Pham & Xavier Warin, 2021. "Rate of convergence for particle approximation of PDEs in Wasserstein space," Papers 2103.00837, arXiv.org, revised Nov 2021.
    • Handle: RePEc:arx:papers:2103.00837
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    File URL: http://arxiv.org/pdf/2103.00837
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    Cited by:

    1. Maximilien Germain & Huyên Pham & Xavier Warin, 2021. "Neural networks-based algorithms for stochastic control and PDEs in finance ," Post-Print hal-03115503, HAL.

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