[Statlist] ETH Young Data Science Researcher Seminar Zurich, Virtual Seminar by Johannes Wiesel, Columbia University

[Maurer Letizia]

Dear all

We are glad to announce the following talk in the virtual ETH Young Data Science Researcher Seminar Zurich

"Estimating processes in adapted Wasserstein distance“  
by Johannes Wiesel, Columbia University 

Time: Friday, 21 May 2021, 15.00 - 16.00
Place: Zoom at  https://ethz.zoom.us/j/97914933906

Abstract: A number of researchers have independently introduced topologies on the set of laws of stochastic processes that extend the usual weak topology. Depending on the respective scientific background this was motivated by applications and connections to various areas (e.g. Plug-​Pichler - stochastic programming, Hellwig - game theory, Aldous - stability of optimal stopping, Hoover-​Keisler - model theory). Remarkably, all these seemingly independent approaches define the same adapted weak topology in finite discrete time. Our first main result is to construct an adapted variant of the empirical measure that consistently estimates the laws of stochastic processes in full generality. A natural compatible metric for the weak adapted topology is the given by an adapted refinement of the Wasserstein distance, as established in the seminal works of Pflug-​Pichler. Specifically, the adapted Wasserstein distance allows to control the error in stochastic optimization problems, pricing and hedging problems, optimal stopping problems, etc. in a Lipschitz fashion. The second main result of this talk yields quantitative bounds for the convergence of the adapted empirical measure with respect to adapted Wasserstein distance. Surprisingly, we obtain virtually the same optimal rates and concentration results that are known for the classical empirical measure wrt. Wasserstein distance. Lastly we construct a coefficient of association as an application of the above theory. This talk is based on joint work with Julio Backhoff, Daniel Bartl and Mathias Beiglböck.

M. Azadkia, Y. Chen, G. Chinot, M. Löffler, A. Taeb

Seminar website: https://math.ethz.ch/sfs/news-and-events/young-data-science.html

Young Data Science Researcher Seminar Zurich – Seminar for Statistics | ETH Zurich
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