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arXiv · 2103.00837

Rate of convergence for particle approximation of PDEs in Wasserstein space

Maximilien Germain·Huyên Pham·Xavier Warin
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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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Maximilien Germain, Huyên Pham, Xavier Warin. 2021-03-01. Rate of convergence for particle approximation of PDEs in Wasserstein space. https://arxiv.org/abs/2103.00837

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