Terry Lyons

Director of Oxford-Man Institute, Wallis Professor of Mathematics, University of Oxford

Terry Lyons is the Director of the Oxford-Man Institute. He is the Wallis Professor of Mathematics at the University of Oxford, a Fellow of the Royal Society, President-Designate of the London Mathematical Society, and one of the UK’s leading mathematicians, having made a number of contributions to stochastic analysis. He has been named Schramm Lecturer for 2014 by the Institute of Mathematical Statistics.

His interest in stochastic analysis relates particularly to the control of non-linear systems driven by rough paths. Prime examples of such systems are provided by stochastic differential equations and stochastic systems.

His research on ‘rough paths’ has founded a new field, stimulating an enormous amount of work, allowing breakthroughs in many areas such as numerical analysis. He has a deep understanding of the role of risk in financial markets where he is known for his work on managing uncertainty in volatility, and for developing cubature methods as new tools allowing more efficient numerical modelling.

Related Events

Stochastic Differential Equations: Numerical Algorithms and Applications
SPA2015
Stochastic Analysis and Applications

Working Paper

Cass, T. and Lyons, T.J. (2011). Integrability estimates for Gaussian rough differential equations.
Gyurkó, L.G., Lyons, T.J., Kontowski, M. and Field, J. (2013). Extracting information from the signature fo a financial data stream.
Boutaib, Y., Gyurko, L.G., Lyons, T. and Yang, D. (2013). Dimension-free Euler estimates of rough differential equations.
Lyons, T.J. and Yang, D. (2013). On Ito differential equation in rough path theory.
Flint, G., Hambly, B. and Lyons, T. (2014). Discretely sampled signales and the rough Hoff process.
Lyons, T. (2014). Rough paths, Signatures and the modelling of functions on streams.
Flint, G., Hambly, B. and Lyons, T. (2013). Discretely sampled signals and the rough Hoff process.
Lyons, T. and Yang, D. (2013). Recovering pathwise Ito solution from averaged Stratonovich solutions.
Boedihardjo, H., Geng, X., Lyons, T. and Yang, D. (2014). The signature of a rough path: uniqueness.
Lyons, T. (2014). Integration of time-varying cocyclic one-form against rough path.
Yang, D. and Lyons, T. (2013). The partial sum process of orthogonal expansion as geometric rough process with Fourier series as an example---an improvement of Menshov-Rademacher theorem.
Lyons, T. and Yang, D. (2014). Integration of time-varying cocyclic one-forms against rough paths.
Lyons, T. and Hao, Ni (2013). Expected signature of Brownian Motion up to the first exit time from a domain.
Levin, D., Lyons, T. and Ni, H. (2013). Learning from the past, predicting the statistics for the future, learning an evolving system.
Lyons, T. and Hao, N. (2011). Expected signature of two dimensional Brownian Motion up to the first exit time of the Domain.
Lyons, T., Cass, T. and Litterer, C. (2011). Integrability estimates for Gaussian rough differential equations.

Published Research

Gyurko, L.G. and Lyons, T.J. (2008). Rough paths based numerical algorithms in computational finance.
Lyons, T.J. (2010). A personal perspective on Raghu Varadhan's role in the development of Stochastic Analysis. In: Holden, H. and Piene, R. The Abel Prize: 2003-2007 The First Five Years, Part 6. Springer. 289-314.
Cass, T., Litterer, C. and Lyons, T. (2011). New Trends in Stochastic Analysis and Related Topics. tbc: World Scientific Publishing. tbc.
Liang, G., Lyons, T. and Qian, Z. (2011). Backward stochastic dynamics on a filtered probability space. Annals of Probability. 39 (4). 1422-1448.
Lyons, T., Cass, T. and Litterer, C. (2011). New Trends in Stochastic Analysis and Related Topics. tbc: World Scientific Publishing. tbc.
Lyons, T. and Litterer, C. (2011). The Oxford Handbook for Non-Linear Filtering. tbc: Oxford University Press. 786-798.
Lyons, T. and Gyurko, L.G. (2011). Efficient and practical implementations of Cubature on Wiener Space. Stochastic Analysis. tbc. 73-111.
Litterer, C. and Lyons, T. (2011). Introducing cubature of filtering . Oxford Handbook of Non-Linear Filtering. tbc. 786-798.
Hambly, B.M. and Lyons, T.J. (2010). Uniqueness for the signature of a path of bounded variation and the reduced path space. Annals of Mathematics. 171 (1). 109-167.
Gyurko, L.G. and Lyons, T. (2009). Rough paths based numerical algorithms in computational finance. In: Menendez, S.C. and Perez, J.L.F Mathematics in Finance. America: AMS. 17-46.
Levin, D. and Lyons, T. (2009). A signed measure on rough paths associated to a PDE of high order: Results and conjectures . Revista Matematica Iberoamericana. 25 (3). 971-994.
Hara, K. and Lyons, T. (2007). Smooth rough paths and applications for Fourier analysis. Revista Matematica Iberiamericana. 23 (3). 1125-1140.
Lyons, T. and Victoir, N (2007). An extension theorem to rough paths. Annales de l'Institut Henri Poincare (C) Non Linear Analysis. 24 (5). 835-847.
Lyons, T. and Ni, H. (2015). Expected signature of Brownian motion up to the first exit time from a domain. Annals of Probability. In Press. TBC.
Lyons, T. Ni, H. and Oberhauser, H. (2014). A feature set for streams and a demonstration on high-frequency financial tick data. Proceedings of the 2014 International Conference on Big Data Science and Computing. New York, NY, USA: ACM. Article 5.