Speaker
Daniela Tonon
(Università degli Studi di Padova)
Description
In this talk, we present a unified approach to Hamilton–Jacobi equations on the Wasserstein space of probability measures arising from deterministic and stochastic dynamics. We introduce a viscosity-solution framework encompassing both first-order equations and semilinear equations driven by idiosyncratic noise. The framework relies on a suitable notion of subdifferential designed to ensure comparison and stability. We then discuss the vanishing-viscosity limit for semilinear Hamilton–Jacobi equations, proving convergence to the corresponding first-order equation as the noise intensity vanishes, with an optimal convergence rate. These results provide a PDE-level characterization of the zero-noise transition.
Author
Daniela Tonon
(Università degli Studi di Padova)