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arXiv · 2608.30493

McKean-Vlasov Differential Equations: An introduction and a focus on some kinetic models

Stefano Pagliarani
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Abstract

These notes were prepared for a series of lectures delivered at the 43rd Finnish Summer School on Probability and Statistics, held in Lammi, Finland, from May 26 to 30, 2025. They provide an introduction to McKean-Vlasov stochastic differential equations and their connections with non-linear Fokker-Planck equations and mean-field interacting particle systems. Particular attention is devoted to density-dependent equations and to kinetic-type models with degenerate noise. For the latter, we introduce the underlying non-Euclidean geometry and the associated anisotropic and intrinsic H\"older spaces, and present well-posedness and regularity results based on Schauder estimates and superposition principles.

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Stefano Pagliarani. 2026-08-31. McKean-Vlasov Differential Equations: An introduction and a focus on some kinetic models. https://arxiv.org/abs/2608.30493

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