Mc Kean-Vlasov stochastic differential equations and mean-field limit of systems of interacting stochastic particles

D. Talay

Last updated on Jan 5, 2022

The aim of this course is to introduce the nonlinear stochastic differential equations in the McKean-Vlasov sense, the chaos propagation of the corresponding particle systems, as well as some techniques for dealing with singular interactions. The emphasis will be on nonlinear martingale problems and the Kokker-Planck-McKean-Vlasov equations.

The approximate outline of the course is as follows:

  1. Various prerequisites: martingale problems, scattering density estimates, Wasserstein distances.
  2. Nonlinear stochastic differential equations in the McKean-Vlasov sense with regular interactions.
  3. Particle systems with McKean-Vlasov interactions: well-posedness and chaos propagation.
  4. Openings to models with singular interactions.

References:

Several sources are partially used, in particular the beginning of the A-S. Sznitman’s course in Saint-Flour, and various works by M. Bossy, B. Jourdain, S. Méléard and myself. The course will emphasize the back and forth between probability and PDE.