Lyons, Professor Terry


Terry Lyons

Supernumerary Fellow and GB member


Personal Website

Academic background

Professor Terry Lyons FRSE FRS is a mathematician, specializing in stochastic analysis. He is the Wallis Professor of Mathematics, a supernumerary fellow of St Anne’s College, Oxford and a Faculty Fellow at The Alan Turing Institute. He was the director of the Oxford-Man Institute from 2011 to 2015 and the president of the London Mathematical Society from 2013 to 2015. His mathematical contributions have been to probability, harmonic analysis, the numerical analysis of stochastic differential equations, and quantitative finance. In particular he developed what is now known as the theory of rough paths.

He received his BA at Trinity College, Cambridge and his DPhil from the University of Oxford.

Research interests

His long-term research interests are all focused on Rough Paths, Stochastic Analysis, and applications – particularly to Finance and more generally to the summarsing of large complex data. That is to say he is interested in developing mathematical tools that can be used to effectively model and describe high dimensional systems that exhibit randomness. This involves him in a wide range of problems from pure mathematical ones to questions of efficient numerical calculation.

Selected publications

Signature features with the visibility transformation
Wu, Y; Ni, H; Lyons, T; Hudson, R
2020 25th International Conference on Pattern Recognition (ICPR) volume 2021 page 4665-4672(5 May 2021) 

Continuity in $κ$ in $SLE_κ$ theory using a constructive method and Rough Path Theory
Beliaev, D; Lyons, T; Margarint, V
L’Institut Henri Poincare, Annales B: Probabilites et Statistiques 

Learning to detect bipolar disorder and borderline personality disorder with language and speech in non-clinical interviews
Wang, B; Wu, Y; Taylor, N; Lyons, T; Liakata, M; Nevado-Holgado, A; Saunders, K
Proceedings of the Annual Conference of the International Speech Communication Association, INTERSPEECH 2020 page 437-441 (16 November 2020) 

Universal approximation with deep narrow networks
Kidger, P; Lyons, T
Proceedings of the 33rd Annual Conference on Learning Theory (COLT 2020) issue 2020 volume 125 page 2306-2327 (6 August 2020) 

Utilisation of the signature method to identify the early onset of sepsis from multivariate physiological time series in critical care monitoring
Morrill, J; Kormilitzin, A; Nevado-Holgado, A; Swaminathan, S; Howison, S; Lyons, T
Critical Care Medicine (3 August 2020) 


High order recombination and an application to cubature on Wiener space
Litterer, C; Lyons, T
Annals of Applied Probability volume 22 page 1301-1327 (2012)

Backward stochastic dynamics on a filtered probability space
Liang, G; Lyons, T; Qian, Z
Annals of Probability issue 4 volume 39 page 1422-1448 (1 July 2011)

Expected signature of two dimensional Brownian Motion up to the first exit time of the domain
Lyons, T; Ni, H

Integrability Estimates for Gaussian Rough Differential Equations
Cass, T; Litterer, C; Lyons, T

Uniqueness for the signature of a path of bounded variation and the reduced path group
Hambly, B; Lyons, T
Annals of Mathematics. Second Series volume 171 page 109-167 (2010)

See more on the Mathematical Institute page.