Mie Gluckstad

Abstract

Randomized signatures were first introduced by C. Cuchiero, L. Gonon, L. Grigoryeva, J.P. Ortega and J. Teichmann in 2021, and have since then been used in the theory of reservoir computing. Based on a proof sketch by E. Akyildirim, M. Gambara, J. Teichmann and S. Zhou from 2022, we prove how to reconstruct the signature components of a path from randomized signatures developed on R^N considered across different initial values, utilizing a path-wise Taylor expansion. The main component of the proof comes down to establishing linear independence between iterated vector fields, which we prove by an algebraic approach. We then discuss extensions of these results to randomized signatures developed on Lie groups. The talk is based on ongoing joint work with Nicola Muça Cirone (Imperial College London) and Josef Teichmann (ETH Zürich). 

Our speaker

Mie Glückstad is a first year DPhil student at the EPSRC CDT Mathematics of Random Systems, based at the University of Oxford. She holds an MSc in Mathematics from the University of Copenhagen and did her master’s thesis under the joint supervision of Prof. Thomas Mikosch (University of Copenhagen) and Prof. Josef Teichmann (ETH Zürich) on rough paths and signature developments on Lie groups.

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