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

Hao, N. and Lyons, T. (2011) Expected signature of Brownian motion up to the first exit time of the domain.

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 , and , (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.
Levin, D. Lyons, T. and Ni, H. (2013). Learning from the past, predicting the statistics for the future and learning an evolving system.
Lyons, T. and Yang, D. (2013). Recovering Pathwise Ito Solution from Averaged Stratonovich Solutions.
Oberhauser, H. Ni, H. and Lyons, T. (2014). A feature set for streams and an application to high-frequency financial tick data.
Levin, D. Lyons, T. and Ni, Hao. (2013). Learning from the past, predicting the statistics for the future, learning an evolving system.
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.

Published Research

Cass, T., Litterer, C. and Lyons, T. (2011) Rough paths on manifolds. In: New Trends in Stochastic Analysis and Related Topics, World Scientific Publishing.

Liang, G., Lyons, T. and Qian, Z. (2011). Liang, G., Lyons, T. and Qian, Z. (2011) Backward stochastic dynamics on a filtered probability space. Annals of Probability. 39 (4), 1422-1448.. Annals of Probability .
Lyons, T. and Hao, N. (2011). Lyons, T. and Hao, N. (2011) Expected Signature of Two Dimensional Brownian Motion up to the First Exit Time of the Domain, Working Paper, Mathematical Institute, University of Oxford, Oxford..
Lyons, T., Cass, T. and Litterer, C. (2011). Lyons, T., Cass, T. and Litterer, C. (2011) Integrability Estimates for Gaussian Rough Differential Equations, Working Paper, Mathematical Institute, University of Oxford, Oxford..

Lyons, T., Cass, T. and Litterer, C. (2011) Rough Paths on Manifolds. In:  Zhao, H. and Truman A., New Trends in Stochastic Analysis and Related Topics. World Scientific Publishing.

Lyons, T. and Litterer, C. (2011). Lyons, T. and Litterer, C. (2011) Introducing Cubature to Filtering. In: Crisan, D. and Rozovskii B., The Oxford Handbook for Non-Linear Filtering. Oxford University Press. 786-798.. The Oxford Handbook for Non-Linear Filtering, OUP.
Lyons, T. and Gyurko, L.G. (2011). Lyons, T. and Gyurko, L.G. (2011) Efficient and Practical Implementations of Cubature on Wiener Space. Stochastic Analysis 2010, 73-111.. Stochastic Analysis 2010.
Gyurkó, L.G. and Lyons, T.J. (2009). Gyurkó, L.G. and Lyons, T.J. (2008) Rough Paths Based Numerical Algorithms in Computational Finance. In: Menendéz, S.C., Pérez, J.L.F., Mathematics in Finance, American Mathematical Society, 17-46.. Rough Paths Based Numerical Algorithms in Computational Finance.
Hambly, B.M. and Lyons, T.J. (2010). 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.. Annals of Mathematics, 171 (1), 109-167. .
Hara, K. and Lyons, T. (2007). Hara, K. and Lyons, T. (2007) Smooth rough paths and applications for Fourier analysis. Revista Matemática Iberoamericana, 23 (3), 1125-1140.. Revista Matemática Iberoamericana, 23 (3), 1125-1140. .
Levin, D. And Lyons, T. (2009). Levin, D. And Lyons, T. (2009) A Signed Measure on Rough Paths Associated to a PDE of High Order: Results and Conjectures. Revista Matemática Iberoamericana, 25 (3), 971-994.. Revista Matemática Iberoamericana, 25 (3), 971-994..
Levin, D. And Lyons, T. (2009). Levin, D. And Lyons, T. (2009) A Signed Measure on Rough Paths Associated to a PDE of High Order: Results and Conjectures. Revista Matemática Iberoamericana, 25 (3), 971-994.. Revista Matemática Iberoamericana, 25 (3), 971-994..
Liang, G., Lyons, T. and Qian, Z. (2011). Liang, G., Lyons, T. and Qian, Z. (2011) Backward Stochastic Dynamics on a Filtered Probablity Space. Annals of Probability, 39 (4), 1422-1448.. Annals of Probability, 39 (4), 1422-1448..
Litterer, C. and Lyons, T. (2011). Litterer, C. and Lyons, T. (2011) Introducing Cubature of Filtering. In: Crisan D. and Rozovsky, B., Oxford Handbook of Non-Linear Filtering. Oxford, Oxford University Press.. In: Crisan D. and Rozovsky, B., Oxford Handbook of Non-Linear Filtering. Oxford, Oxford University Press..
Lyons, T., and Victoir, N. (2007). Lyons, T., and Victoir, N. (2007) An extension theorem to rough paths. Annales de l’Institut Henri Poincaré (C) Non Linear Analysis, 24 (5), 835-847.. Annales de l’Institut Henri Poincaré (C) Non Linear Analysis, 24 (5), 835-847..
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.
Lyons, T. Ni, H. and Oberhauser, H. (2014). ACM Proceedings "Big Data Science 2014, Beijing" . Forthcoming. TBC. TBC.