Brownian motions on spaces of probability measures
Date
Thursday, October 31, 2019 16:00 - 18:00
Speaker
Lorenzo Dello Schiavo (University of Bonn)
Location
Heinzel Seminar Room / Office Bldg West (I21.EG.101)
Series
Seminar/Talk
Tags
Mathematics and CS Seminar, mathematical_seminar_ics
Host
Jan Maas
Contact
A diffusion process is constructed on the L2-Wasserstein space over a closed Riemannian manifold. The process, which may be regarded as a candidate for the Brownian motion on such space, is associated with the Dirichlet form induced by the L2-Wasserstein gradient and by the DirichletFerguson random measure with intensity the Riemannian volume measure on the base manifold. We discuss the closability of the form via an integration-by-parts formula, which allows explicit computations for the generator and a specification of the process via a measure-valued SPDE. We comment how the construction is related to previous work of von RenesseSturm on the Wasserstein Diffusion and of Konarovskyivon Renesse on the Modified Massive Arratia Flow.