The collaborative research center TRR 388 "Rough Analysis, Stochastic Dynamics & Related Fields" started on the 1st of October, 2024. The three applicant universities are TU Berlin, HU Berlin and FU Berlin.

Stochastic dynamics builds on probability theory and Itô’s stochastic analysis to study the evolution of systems under the influence of randomness, and has flourished for decades with profound impact on many fields, including statistical physics, mathematical finance, uncertainty quantification, quantum field theory, mathematical biology, economics.

Rough analysis, on the other hand, stands for recent breakthroughs in mathematics, rooted in Lyons’ rough path theory. With the original motivation of introducing robustness in noise/signal, rough analysis offers a nonlinear extension of distribution theory that is crucial for understanding singular stochastic dynamics and their possible renormalizations, and to capture nonlinear effects of signals. Transcending its origins, rough analysis recently saw the emergence of deep mathematical structures with significant geometric and algebraic components.

Together, they form the fertile grounds for this TRR Rough Analysis, Stochastic Dynamics and Related Fields.

With an intense interplay of analysis, algebra/geometry and probability theory together with closely related applied topics, such as statistics, robust modeling under uncertainty, and stochastic control theory and mathematical finance, the overarching goal of this TRR is to foster mutually beneficial interactions with the new field of rough analysis.