Date: Thursday, 12 March 2026
Speakers: Eduardo Abi Jaber (Ecole Polytechnique)
Title: Path-Signatures: Memory and Stationarity
Abstract: We explore the interplay between path-signatures, memory, and stationarity, highlighting their implications for machine learning, representation of stochastic processes and applications in mathematical finance. In a first part, we provide explicit series expansions to certain stochastic path-dependent integral equations in terms of the path signature of the time augmented driving Brownian motion. Our framework encompasses a large class of stochastic linear Volterra and delay equations and in particular the fractional Brownian motion with a Hurst index H in (0, 1). Our expressions allow to disentangle an infinite dimensional Markovian structure. In addition they open the door to: (i) straightforward and simple approximation schemes that we illustrate numerically, (ii) representations of certain Fourier-Laplace transforms in terms of a non-standard infinite dimensional Riccati equation with important applications for pricing and hedging in quantitative finance. In a second part, we introduce a time-invariant version of the signature: the fading-memory signature, with powerful algebraic, analytic and probabilistic properties and applications to learning stationary relationships in time series. This is based on joint works with Paul Gassiat, Louis-Amand Gérard, Yuxing Huang, Dimitri Sotnikov.
Thursday, 12 March 2026, 18:00 (GMT +1) – the US is switching to daylight saving time on 8 March
Link to registration:
https://siam.zoom.us/webinar/register/WN_s8rIcHwiS-uPM3Dkuok-Wg
