Set-valued propagation of chaos for controlled path-dependent McKean-Vlasov SPDEs
Abstract
We develop a limit theory for controlled path-dependent mean field stochastic partial differential equations (SPDEs) within the semigroup approach of Da Prato and Zabczyk. More precisely, we prove existence results for mean field limits and particle approximations, and we establish set-valued propagation of chaos in the sense that we show convergence of sets of empirical distributions to sets of mean field limits in the Hausdorff metric topology. Furthermore, we discuss consequences of our results to stochastic optimal control. As another application, we deduce a propagation of chaos result for Peng's -Brownian motion with drift interaction.
Keywords
Cite
@article{arxiv.2312.08331,
title = {Set-valued propagation of chaos for controlled path-dependent McKean-Vlasov SPDEs},
author = {David Criens and Moritz Ritter},
journal= {arXiv preprint arXiv:2312.08331},
year = {2026}
}
Comments
Results have been extended to random initial conditions and relation to other control frameworks are explained