Curvature condition for the stability of SDEs on the Wasserstein space

par Aymeric Martin (Université de Bordeaux)

mardi 3 nov. 2026, 09:50 → 10:50 Europe/Paris

In 2013, Cattiaux and Guillin introduce the so-called HC(K) condition for $K \in \mathbb{R}$ on the drift and the diffusion coefficients of an $\mathbb{R}^d$-valued SDE to study the stability of the latter (Ergodicity, speed of convergence, functional inequalities…). We present a generalization of this condition, the IWCD(K) condition, on the Wasserstein space over a closed Riemannian manifold, which depends on the driving vector fields of the SDE but also on the instrinsic Riemann curvature of the Wasserstein space. In particular, when $K>0$, we obtain the existence and uniqueness of an ergodic invariant measure for the associated Markov semigroup.