Set-valued propagation of chaos for controlled path-dependent McKean-Vlasov SPDEs

David Criens; Moritz Ritter

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arXiv · 2312.08331

Set-valued propagation of chaos for controlled path-dependent McKean-Vlasov SPDEs

David Criens·Moritz Ritter

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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 $G$-Brownian motion with drift interaction.

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BibTeX RIS

David Criens, Moritz Ritter. 2023-12-13. Set-valued propagation of chaos for controlled path-dependent McKean-Vlasov SPDEs. https://arxiv.org/abs/2312.08331

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