Abstract

This talk starts with basic Riemann vs Lebesgue integration, turning then to stochastic and rough integration. We then develop the concept of rough Itô processes, which extend stochastic calculus to accommodate rough stochastic differential equations (SDEs) and their mean-field counterparts. These structures provide a natural setting for stochastic modelling under partial conditioning of the noise. Concrete applications include non-linear filtering, pathwise stochastic control theory, local stochastic volatility modelling, and interacting particle systems with common noise.  The presentation aims to bridge classical and modern integration techniques, demonstrating their relevance in contemporary stochastic and rough analysis. 

Biography

Peter Friz is Einstein Professor of Mathematics at the Technische Universität Berlin and the Weierstraß Institute for Applied Analysis and Stochastics. He holds degrees from Vienna, Paris, Trinity College Cambridge and a PhD from Courant Institute at NYU. Professional appointments include Merrill Lynch, New York, a Readership at Cambridge University, Visiting Professorships at ETH Zurich, Ecole Polytechnique Paris and Shandong University. For his work on quantitative finance, stochastics and rough analysis, including several monographs, he has received repeated ERC awards. Peter has served the community as co-editor-in-chief for the Annals of Applied Probability; as of 2024, he heads a new Berlin based DFG collaborative research center on `Rough Analysis and Stochastic Dynamics'.