PreprintCC BY 4.0arXiv
McKean-Vlasov Differential Equations: An introduction and a focus on some kinetic models
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 Hölder spaces, and present well-posedness and regularity results based on Schauder estimates and superposition principles.
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BibTeX
@misc{pagliarani2026mckeanvlasov,
title = {{McKean-Vlasov Differential Equations: An introduction and a focus on some kinetic models}},
author = {Stefano Pagliarani},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.30493},
eprint = {2608.30493},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.30493},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - McKean-Vlasov Differential Equations: An introduction and a focus on some kinetic models
AU - Stefano Pagliarani
PY - 2026
DA - 2026/08/31
PB - arXiv
DO - 10.48550/arxiv.2608.30493
UR - https://arxiv.org/abs/2608.30493
AB - 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 Hölder spaces, and present well-posedness and regularity results based on Schauder estimates and superposition principles.
ER -