English

Convergence Rate of Particle System for Second-order PDEs On Wasserstein Space

Analysis of PDEs 2025-01-15 v2

Abstract

In this paper, we provide a convergence rate for particle approximations of a class of second-order PDEs on Wasserstein space. We show that, up to some error term, the infinite-dimensional inf(sup)-convolution of the finite-dimensional value function yields a super (sub)-viscosity solution to the PDEs on Wasserstein space. Hence, we obtain a convergence rate using a comparison principle of such PDEs on Wasserstein space. Our argument is purely analytic and relies on the regularity of value functions established in \cite{DaJaSe23}.

Keywords

Cite

@article{arxiv.2408.06013,
  title  = {Convergence Rate of Particle System for Second-order PDEs On Wasserstein Space},
  author = {Erhan Bayraktar and Ibrahim Ekren and Xin Zhang},
  journal= {arXiv preprint arXiv:2408.06013},
  year   = {2025}
}