The Ornstein$-$Uhlenbeck process on ${\mathcal{P}}_2$ with a volatility operator

Martin Grothaus, Simon Wittmann

We analyze a diffusion ${({\mu }_t)}_{t\ge 0}$ on the $2$-Wasserstein space ${\mathcal{P}}_2$ over ${\mathbb{R}}^d$ for which \begin{equation*} |μ_t|_2^2-|μ_0|_2^2-2ct+2\int_0 ^t|μ_s|_2^2\,d…