Stochastic particle systems and McKean-Vlasov models: Theory and Applications

McKean-Vlasov models define a class of stochastic evolution equations which arise from the probabilistic interpretation of nonlinear physical and biological systems and from the large-population asymptotic of particle systems in mean-field interactions. Originally introduced in the sixties, the theoretical and practical interests for McKean-Vlasov models have been extensively invigorated over the past fifteen years following the deeper connections between these models and economic and social population dynamics, game theory and control problems and the modeling of efficient machine learning methods. This talk will be dedicated to present the fundamentals of McKean-Vlasov models, from a theoretical and practical point of view, and to discuss the most recent trends related to these models.