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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: Mathematics and CS Seminar
Host: Jan Maas

Abstract:

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.
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