# Terry Lyons

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

## Working Paper

*Expected signature of Brownian motion up to the first exit time of the domain, Working Paper, Mathematical Institute, University of Oxford, Oxford*.

*Integrability estimates for Gaussian rough differential equations*.

*Extracting information from the signature fo a financial data stream*.

*Dimension-free Euler estimates of rough differential equations*.

*On Ito differential equation in rough path theory*.

*Discretely sampled signales and the rough Hoff process*.

*Rough paths, Signatures and the modelling of functions on streams*.

*Discretely sampled signals and the rough Hoff process*.

*Learning from the past, predicting the statistics for the future and learning an evolving system*.

*Recovering pathwise Ito solution from averaged Stratonovich solutions*.

*A feature set for streams and an application to high-frequency financial tick data*.

*The signature of a rough path: uniqueness*.

*Integration of time-varying cocyclic one-form against rough path*.

*The partial sum process of orthogonal expansion as geometric rough process with Fourier series as an example---an improvement of Menshov-Rademacher theorem*.

*Integration of time-varying cocyclic one-forms against rough paths*.

*Expected signature of Brownian Motion up to the first exit time from a domain*.

*Learning from the past, predicting the statistics for the future, learning an evolving system*.

## 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.

*Annals of Probability*.

*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) 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.

*The Oxford Handbook for Non-Linear Filtering, OUP*.

*Stochastic Analysis 2010*.

*Rough Paths Based Numerical Algorithms in Computational Finance*.

*Annals of Mathematics, 171 (1), 109-167.*.

*Revista Matemática Iberoamericana, 23 (3), 1125-1140.*.

*Revista Matemática Iberoamericana, 25 (3), 971-994.*.

*Revista Matemática Iberoamericana, 25 (3), 971-994.*.

*Annals of Probability, 39 (4), 1422-1448.*.

*In: Crisan D. and Rozovsky, B., Oxford Handbook of Non-Linear Filtering. Oxford, Oxford University Press.*.

*Annales de l’Institut Henri Poincaré (C) Non Linear Analysis, 24 (5), 835-847.*.

*Rough paths based numerical algorithms in computational finance*.

*The Abel Prize: 2003-2007 The First Five Years, Part 6*. Springer. 289-314.