发表机构
Università di Bologna（博洛尼亚大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本讲义为芬兰概率与统计暑期学校讲座准备，介绍McKean-Vlasov微分方程，重点研究带退化噪声的动力学模型，给出其相关几何空间及适定性、正则性结果。
AI 中文摘要
本讲义为2025年5月26日至30日在芬兰兰米举办的第43届芬兰概率与统计暑期学校系列讲座准备，介绍McKean-Vlasov随机微分方程及其与非线性Fokker-Planck方程、平均场相互作用粒子系统的联系，重点关注依赖密度的方程及带退化噪声的动力学型模型；针对后者，引入相关的非欧几何、各向异性与内在Hölder空间，并基于Schauder估计和叠加原理给出适定性与正则性结果。
英文摘要
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.
