This will be an extension of the reading group on the same topics in Spring 2025. Topics are to be determined. Feel free to reach out if you are interested.
Time: T.B.D., but very likely bi-weekly on Friday afternoon
Contents: Preliminary plans: Signature-based models in finance; Branched rough paths for arbitrarily irregular paths (in Hölder sense); Neural RDE/CDE; Jump processes as scaling limit of (hyper-)rough processes; Signature methods for solving games numerically; Wiener Chaos Expansions via Signatures;... (To be updated upon participants' interests.)
Calendar:
T.B.D. but very likely to be held bi-weekly
References:
Ilya Chevyrev, Andrey Kormilitzin, A Primer on the Signature Method in Machine Learning, 2016
Lajos Gergely Gyurk, Terry Lyons, Mark Kontkowski, and Jonathan Field, Extracting information from the Signature of a Financial Data Stream, 2014
Thomas Cass, Cristopher Salvi, Lecture Notes on Rough Paths and Applications to Machine Learning, 2024
Peter Friz, Martin Hairer, A Course on Rough Paths with an Introduction to Regularity Structures, 2020
Terry Lyons, Andrew Mcleod, Signature Methods in Machine Learning, 2022
Christa Cuchiero, Guido Gazzani, Sara Svaluto-Ferro, Signature-based Models: Theory and Calibration, 2023
Adeline Fermanian, Terry Lyons, James Morrill, Cristopher Salvi, New Directions in the Applications of Rough Path Theory, 2023
Others (to be updated)...
Special thanks to Professor Tomoyuki Ichiba and Professor Ruimeng Hu for offering valuable suggestions on the organisation and contents of this reading group.