Project A02
Optimal transport meets rough analysis

Project description

The theories of Optimal Transport (OT) and Rough Analysis, pivotal in both analysis and probability theory, are to be explored for their interplay. Our research includes studying optimal transport of Gaussian measures in Carnot groups and on rough path spaces. Additionally, we analyze Wasserstein rates for rough volatility models and singular Langevin systems in a metric gradient flow, focusing on the dynamic Φ^4_d model. The objective is to uncover new insights for OT through Rough Analysis and vice versa. 

Principal Investigators

Peter Friz (TU Berlin)

Matthias Liero (WIAS)

Project members

Helena Kremp (WIAS & TU Berlin)

Publications

• Friz, P.K., Kern, H., Zorin-Kranich, P., 2025. Lipschitz estimates in the Besov settings for Young and rough differential equations. Journal of Differential Equations 443, 113507. https://doi.org/10.1016/j.jde.2025.113507 (A02, A07, B04)

• Friz, P.K., Gatheral, J., 2025. Computing the SSR. Quantitative Finance 1–10. https://doi.org/10.1080/14697688.2025.2486173

Preprints

• Friz, P. K., Hager, P. P., 2025. Expected Signature Kernels for Lévy Rough Paths. https://doi.org/10.48550/ARXIV.2509.07893 (A02, A05)

• Liero, M., Mielke, A., Tse, O., Zhu, J.-J., 2025. Evolution of Gaussians in the Hellinger-Kantorovich-Boltzmann gradient flow. https://doi.org/10.48550/ARXIV.2504.20400