DataScience@BI seminar with Dimitri Sotnikov
DataScience@BI seminar invites Dimitri Sotnikov, École polytechnique & ENGIE Global Markets, to talk about "Chasing Stationarity: Exponentially Fading Memory Signature".
- Starts:12:00, 3 March 2026
- Ends:13:00, 3 March 2026
- Location:BI - campus Oslo, B3 inner area - next to meeting room B3i-108 or Zoom
- Contact:Siri Johnsen (siri.johnsen@bi.no)
Abstract
We introduce the exponentially fading memory (EFM) signature, a time-invariant transformation of an infinite (possibly rough) path that serves as a mean-reverting analogue of the classical path signature. We construct the EFM-signature via rough path theory, carefully adapted to accommodate improper integration from minus infinity. The EFM-signature retains many of the key algebraic and analytical properties of classical signatures, including a suitably modified Chen identity, the linearization property, path-determinacy, and the universal approximation property. From the probabilistic perspective, the EFM-signature provides a "stationarized" representation, making it particularly well-suited for time-series analysis and signal processing overcoming the shortcomings of the standard signature. In particular, the EFM-signature of time-augmented Brownian motion evolves as a group-valued Ornstein-Uhlenbeck process. We establish its stationarity, Markov property, and exponential ergodicity in the Wasserstein distance, and we derive an explicit formula à la Fawcett for its expected value in terms of Magnus expansions. This is joint work with Eduardo Abi Jaber.
Key research areas: Path signatures, non-Markovian models in mathematical finance
The DataScience@BI seminar is organised by the Department of Data Science and Analytics, BI Norwegian Business School.