Arthur Schichl, ETH Zürich

Title: Non-linear Degenerate Parabolic Flow Equations and a Finer Differential Structure on Wasserstein Spaces

Abstract: We define new differential structures on the Wasserstein spaces W_p(M) for p > 2 and a Riemannian manifold (M,g). We consider a very general and possibly degenerate second-order partial differential flow equation with measure dependent coefficients to expand the notion of smooth curves and to ensure that the new differential structure is finer than the classical one. The theory allows for higher order calculus on Wasserstein spaces and admits numerical approximations in W_p(M). We prove a generalized version of the Central Limit Theorem without requiring independence. We shall also present some of its economic applications.