Superposition principles for random measures and applications
A talk in the Bielefeld Stochastic Afternoon series by
Alessandro Pinzi
| Abstract: | I will present a new proof of the superposition principle of Lacker--Shkolnikov--Zhang in the particular case where the Kolmogorov--Fokker--Planck equation is deterministic, allowing for more general integrability conditions. I will then discuss some implications of this result. First, I will explain how to transfer uniqueness between the equations. Next, together with a metric superposition principle in the spirit of Lisini’s lifting, we will recover a Benamou--Brenier formula and a characterization of the tangent space of the $L^p$-Wasserstein-on-Wasserstein space.Finally, by fixing a suitable reference measure $Q \in \mathcal{P}(\mathcal{P}(\mathbb{R}^d))$ over the Wasserstein space, a refinement of the superposition principle yields new insights on the metric measure space $(\mathcal{P}_p(\mathbb{R}^d),W_p,Q)$. The presentation is partially based on joint work with Giuseppe Savaré. Within the CRC this talk is associated to the project(s): A5 |