The turnpike property, large deviations, and the Schrooedinger problem.

03.06.2019, 12:00  –  Golm, Haus 9, Raum 0.13
Forschungsseminar Wahrscheinlichkeitstheorie

Giovanni Conforti (Ecole Polytechnique)

In deterministic control, the turnpike property is the fact that optimal solutions consist approximatively of three pieces. The first and third pieces are rapid transitions from the initial state to a steady state and from the steady state to the final state respectively. The second piece is a long time interval in which solutions stay exponentially close to the steady state. In this talk I will discuss how to adapt the turnpike property in stochastic control problems arising from large deviations theory and explain why one should expect it to hold. In the second part we look at the concrete example of the Schroedinger, for which the turnpike property holds. If time allows, I will treat the case of the recently introduced mean field Schroedinger problem.