Imperial College London


Faculty of Natural SciencesDepartment of Mathematics

Reader in Stochastic Analysis







808Weeks BuildingSouth Kensington Campus





Thomas Cass is a Reader in the Mathematics Department at Imperial College London.  He obtained his MA and PhD from Department of Pure Mathematics and Mathematical Statistics, the University of Cambridge. 

Thomas' research interests relate to the study of random phenomena. His research writings span both classical areas of stochastic analysis such as Malliavin calculus, and newly-emerging disciplines such as Rough Path Theory. He is also interested in the way in which deep insights in Pure Mathematics can spur developments in Mathematical Finance, especially numerical techniques. A more specific list of his interests include:

* The theory of Rough Paths and Rough Differential Equations (RDEs), both deterministic and stochastic.

* Gaussian processes, fractional Brownian motion and the properties of RDEs driven by these processes. 

*  The use of Malliavin calculus and cubature on Wiener space for sensitivity analysis and efficient pricing and hedging methods in Mathematical Finance.

*  McKean-Vlasov-type models for large populations of interacting agents with individual preferences.

*  Stochastic differential geometry and rough paths on manifolds. 

*  Applications of stochastic analysis in cardio-electrophysiology.

Teaching: Stochastic Differential Equations (M5MF47/M5MR11)

Advanced topics in stochastic analysis

Selected Publications

Journal Articles

Cass T, Litterer C, Lyons T, 2013, Integrability and tail estimates for Gaussian rough differential equations, Annals of Probability, Vol:41, Pages:3026-3050

Cass T, Hairer M, Litterer C, et al., 2012, Smoothness of the density for solutions to Gaussian Rough Differential Equations

Cass T, Friz, P., 2010, Densities for rough differential equations under Hörmander’s condition, Annals of Mathematics, Vol:171, ISSN:0003-486X, Pages:2115-2141

Cass T, 2009, Smooth densities for solutions to stochastic differential equations with jumps, Stochastic Processes and Their Applications, Vol:119

Cass T, Friz P, Victoir N, 2009, Non-degeneracy of Wiener functionals arising from rough differential equations, Transactions of the American Mathematical Society, Pages:3359-3371


Cass T, Litterer C, Lyons T, 2012, Rough Paths on Manifolds, New trends in stochastic analysis and related topics, 33–88,,, Editor(s): Zhao, Truman, World Scientific Publishing Company, Pages:33-88, ISBN:9789814360913

More Publications