A limit theory for controlled McKean-Vlasov SPDEs

TL;DR

This paper develops a limit theory for controlled mean field SPDEs, establishing existence, particle approximations, and propagation of chaos, with applications to stochastic porous media systems.

Contribution

It introduces a variational framework for controlled mean field SPDEs, proving new existence results and set-valued convergence theorems.

Findings

Proved existence of mean field limits and particle approximations.

Established set-valued propagation of chaos in Hausdorff topology.

Applied theory to controlled stochastic porous media equations.

Abstract

We develop a limit theory for controlled mean field stochastic partial differential equations in a variational framework. More precisely, we prove existence results for mean field limits and particle approximations, and we establish a set-valued propagation of chaos result which shows that sets of empirical distributions converge to sets of mean field limits in the Hausdorff metric topology. Further, we discuss limit theorems related to stochastic optimal control theory. To illustrate our findings, we apply them to a controlled interacting particle system of stochastic porous media equations.