“Randomized Approach to Mean Field Control”
Giovedì 11 Dicembre 2025, ore 13:30 - Aula 2BC30 - Mattia Martini (Centre de Mathématiques Appliquées (CMAP))
Abstract
This talk aims to show how randomizing the dynamics in mean field control can help regularize the associated Hamilton–Jacobi equation. A key challenge in this approach lies in constructing a suitable notion of noise on the space of probability measures. To this end, we rely on the Dirichlet–Ferguson diffusion process, as studied by Dello Schiavo [AOP 22]. We first examine the effect of this noise on a system of uncontrolled interacting particles and show that it induces a regularizing effect at the level of the corresponding backward Kolmogorov equation. We then analyze a mean field control problem driven by this noise and prove that the associated Hamilton–Jacobi equation admits a unique solution in an appropriate functional space, even when the coefficients have limited regularity.
The talk is based on a joint work with F. Delarue (Nice) and G. Sodini (Vienna).
