Speaker
Description
We study a class of McKean-Vlasov SDEs in a Hilbert space $H$ and prove that the associated transition semigroup (which is defined on a Wasserstein space $\mathcal{P}_p(H)$ for some $p\ge 1$) possesses a smoothing property, i.e., it transforms continuous functions admitting the linear functional derivative $\frac{\delta}{\delta m}$ into functions admitting the measure derivative $D_m$. This generalizes in various ways previous results obtained in the finite-dimensional setting by Chaudru de Raynal and Frikha (Well-posedness for some non-linear SDEs and related PDE on the Wasserstein space, J. Math. Pures Appl., 2022). We then discuss the applications of such results. The talk is based on a joint work (in progress) with A. Calvia and F. Gozzi.