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The Wasserstein space of stochastic processes

Budapest-Vienna Probability Seminar

Date
Wednesday, April 27, 2022 15:00 - 15:50
Speaker
Mathias Beiglböck (University of Vienna)
Location
Heinzel Seminar Room (I21.EG.101), Office Building West
Series
Seminar/Talk
Tags
Mathematics and CS Seminar, mathematical_seminar_ics
Host
M. Beiglböck, N. Berestycki, L. Erdös, J. Maas, F. Toninelli
Contact

Wasserstein distance induces a natural Riemannian structure for the probabilities on the Euclidean space. This insight of classical transport theory is fundamental for tremendous applications in various fields of pure and applied mathematics.
We believe that an appropriate probabilistic variant, the adapted Wasserstein distance AW, can play a similar role for the class FP of filtered processes, i.e. stochastic processes together with a filtration. In contrast to other topologies for stochastic processes, probabilistic operations such as the Doob-decomposition, optimal stopping and stochastic control are continuous w.r.t. AW. We also show that (FP,AW) is a geodesic space, isometric to a classical Wasserstein space, and that martingales form a closed geodesically convex subspace. (Joint work with Daniel Bartl and Gudmund Pammer)


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