Wednesday, October 11, 2023 - 14:15 in V3-201 + Zoom
The Dirichlet–Ferguson Diffusion on the space of probability measures over a closed Riemannian manifold
A talk in the Bielefeld Stochastic Afternoon series by
Lorenzo Dello Schiavo
| Abstract: |
We construct a diffusion process on the $L^2$-Wasserstein space $P_2(M)$
over a closed Riemannian manifold $M$. The process, which may be
regarded as a candidate for the Brownian motion on $P_2(M)$, is
associated with the Dirichlet form induced by the $L^2$-Wasserstein
gradient and by the Dirichlet–Ferguson random measure with intensity
the Riemannian volume measure on $M$. 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 martingale problem. We comment about relations to
previous work of Overbeck–Röckner–Schmuland on the Fleming–Viot
process, of von Renesse–Sturm on the Wasserstein Diffusion, of
Konarovskyi–von Renesse on the Modified Massive Arratia Flow.
Based on Ann. Probab. 50(2):591–648, 2022
Within the CRC this talk is associated to the project(s): A5 |
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