Martedì 20 Dicembre, ore 14:00, Sapienza Università di Roma, Dipartimento
di Matematica, Sala di Consiglio
*Speaker: *Giacomo Greco (Eindhoven University of Technology TU/e)
*Titolo:* Travelling through turnpikes in the Kinetic Schrödinger Problem
*Abstract:* The Schrödinger problem consists in finding the most likely
evolution of a system of i.i.d. particles, conditionally on their initial
and final configurations. In the last decade this problem has become more
and more popular, thanks to its connections with stochastic optimal control
theory and optimal transport. In this talk we are going to introduce a
Schrödinger problem where the particles follow an (underdamped) Langevin
dynamics (i.e. their density satisfies the kinetic Fokker-Planck equation)
and where we are given only a partial observation of the initial and final
configurations. Then, we will investigate the long-time behaviour of this
kinetic system, proving that its most likely evolution is exactly the one
that spends most of the time exponentially close to the equilibrium
configuration (this property is commonly known in stochastic control theory
as the turnpike property). Based on the paper Electron. J. Probab. 27:
1-32 (2022). DOI: 10.1214/22-EJP850