Causal optimal transport for stochastic processes

I will discuss causal transport theory and the adapted Wasserstein distance, which extend classical transport theory from probability measures to stochastic processes by incorporating the temporal flow of information. This adaptation addresses key limitations of classical transport when dealing with time-dependent data. I will highlight how, unlike other topologies for stochastic processes, the adapted Wasserstein distance ensures continuity for fundamental probabilistic operations, including the Doob decomposition, optimal stopping, and stochastic control. Additionally, I will explore how adapted transport preserves many desirable properties of classical transport theory, making it a powerful tool for analysing stochastic systems.

Daniel Bartl is a Presidential Young Assistant Professor of Mathematics, Statistics, and Data Science at the National University of Singapore. His research lies at the intersection of high-dimensional probability, stochastic processes, optimal transport, and robust optimisation. He is particularly interested in distributionally robust methods and their applications in statistics and machine learning.

For more information about the ESD Seminar, please email esd_invite@sutd.edu.sg