# Terry Lyons

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

## Working Paper

*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*.

*Recovering pathwise Ito solution from averaged Stratonovich solutions*.

*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 two dimensional Brownian Motion up to the first exit time of the Domain*.

*Integrability estimates for Gaussian rough differential equations*.

*Uniform factorial decay estimate for the remainder of rough taylor expansion*.

*A set of characteristic functions on the space of signatures*.

*Rough differential equation in Banach space driven by weak geometric p-rough path*.

## Published Research

*Rough paths based numerical algorithms in computational finance*.

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

*New Trends in Stochastic Analysis and Related Topics*. tbc: World Scientific Publishing. tbc.

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

*New Trends in Stochastic Analysis and Related Topics*. tbc: World Scientific Publishing. tbc.

*The Oxford Handbook for Non-Linear Filtering*. tbc: Oxford University Press. 786-798.

*Stochastic Analysis*. tbc. 73-111.

*Oxford Handbook of Non-Linear Filtering*. tbc. 786-798.

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

*Mathematics in Finance*. America: AMS. 17-46.

*Revista Matematica Iberoamericana*. 25 (3). 971-994.

*Revista Matematica Iberiamericana*. 23 (3). 1125-1140.

*Annales de l'Institut Henri Poincare (C) Non Linear Analysis*. 24 (5). 835-847.

*Annals of Probability*. 43 (5). 2729-2762.

*Proceedings of the 2014 International Conference on Big Data Science and Computing*. New York, NY, USA: ACM. Article 5.

*Journal of Mathematical Society of Japan*. Forthcoming. Forthcoming.

*Communications in Mathematical Sciences*. tba. tba.

*Proceedings of the London Mathematical Society*. 110. 83-107.

*Journal of Functional Analysis*. 272(7). 2933-2955.

*Journal of Functional Analysis*. 268(7). 1928-1971.

*Transactions of the American Mathematical Society*. 367. 7939-7955.

*Journal of the European Mathematical Society*. tba. tba.