[PDE & Applications seminar] Katharina Eichinger: On McKean-Vlasov control problems: Turnpike property and propagation of chaos

29 juni 2023 16:00 t/m 17:00 - Locatie: EEMCS-Lecture Hall Ampere (36.HB.01.670) | Zet in mijn agenda

In this talk we provide an analysis for a class of McKean-Vlasov control problems. Our technique is based on coupling by reflection adapted to controlled processes allowing us to treat dynamics consisting of a drift component only being strongly decreasing outside a large ball, and possibly an additional sufficiently small meanfield interaction. With this we prove a uniform in time Lipschitz estimate of the value function and its (measure) derivatives under suitable assumptions. This enables us to prove existence and uniqueness of the ergodic problem and the exponential turnpike property, that is optimal trajectories stay exponentially close to the stationary solution. We also prove uniform in time quantitative propagation of chaos of the dynamics of the corresponding N agent control problem towards its meanfield counterpart.

This is based on a joint work in progress with Alekos Cecchin, Giovanni Conforti and Alain Durmus.