Mean-field particle systems and their limits to non-local PDEs

Lectures: Mo. 10:15 – 11:45 in A 5, 6 – C 013, Di. 13:45 – 15:15 in A 5, 6 – C 013
Tutorial: Mo. 12:00 – 13:30 in A 5, 6 – C 012
Language: English
Prerequisites: Analysis I and II, Linear algebra I, Probability I

It is a master's course, however, all bachelor students who have already “Analysis I and II” are welcome to join.

• Golse, F. (2016). On the dynamics of large particle systems in the mean field limit. In Macroscopic and large scale phenomena: coarse graining, mean field limits and ergodicity (pp. 1–144). Springer, Cham. 1.2–1.5

• Carmona, R. (2016). Lectures on BSDEs, stochastic control, and stochastic differential games with financial applications. Society for Industrial and Applied Mathematics, Chapters 1–2

• Lachker D. (2018). Lecture notes: Mean _eld games and interacting particle systems, Chapters 1–3

Aim of module:

Rigorous derivation of mean-field type PDEs. Topics include:
• Basic existence results for ODE and SDE
• Wellposedness theory of mean-field type nonlocal PDEs
• Entropy estimates for PDEs
• Derivation of kinetic mean-field equation from N particle dynamical system.
• Derivation of diffusion aggregation equation