Terry Lyons

Wallis Professor of Mathematics, University of Oxford

Terry is the Wallis Professor of Mathematics at the University of Oxford, a founding member (2007) of, and then Director (2011-2015) of, the Oxford Man Institute of Quantitative Finance, and the Director of the Wales Institute of Mathematical and Computational Sciences (WIMCS; 2008-2011). Terry came to Oxford in 2000 having previously been Professor of Mathematics at Imperial College London (1993-2000), and before that held the Colin Maclaurin Chair at Edinburgh (1985-93).

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. 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.

 

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, 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.
Boedihardjo, H. Lyons, T. and Yang, D. (2015). Uniform factorial decay estimate for the remainder of rough taylor expansion.
Chevyrev, I. and Lyons, T. (2015). A set of characteristic functions on the space of signatures.
Yang, D. and Lyons, T. (2014). Rough differential equation in Banach space driven by weak geometric p-rough path.

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. 43 (5). 2729-2762.
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.
Lyons, T. and Yang, D. (2015). The theory of rough paths via one-forms and the extension of an argument of Schwartz to rough differential equations. Journal of Mathematical Society of Japan. Forthcoming. Forthcoming.
Lee, W. and Lyons, T (2016). The adaptive patched particle filter and its implementation. Communications in Mathematical Sciences. tba. tba.
Cass, T. and Lyons, T. (2017). Evolving communities with individual preferences. Proceedings of the London Mathematical Society. 110. 83-107.
Xu, W. and Lyons, T. (2017). Hyperbolic development and inversion of signature. Journal of Functional Analysis. 272(7). 2933-2955.
Crisan, D., Litterer, C. and Lyons, T. (2015). Kusuoka--Stroock gradient bounds for the solution of the filtering equation. Journal of Functional Analysis. 268(7). 1928-1971.
Fritz, P., Gassiat, P. and Lyons, T. (2015). Physical Brownian motion in a magnetic field as a rough path. Transactions of the American Mathematical Society. 367. 7939-7955.
Xu, W. and Lyons, T. (2016). Inverting the signature of a path. Journal of the European Mathematical Society. tba. tba.