Terry Lyons, Oxford: "Rough paths"
There will be three lectures, the first will consider the
signature of a path; the second will look at the general theory of rough
paths, explaining the most basic theorems; the third will look at how the
signature of a path, together with a re-combination technique, can be used
to produce high order substitute methods for Monte Carlo. Putting these
ideas together one is able to create a family of novel and very accurate
1. Ben Hambly and Terry Lyons Uniqueness for the signature of a path of
bounded variation and the reduced path group, (to appear Ann. Math)
2. Lyons, Terry J., Caruana, Michael, LÚvy, Thierry Differential Equations
Driven by Rough Paths Ecole d'EtÚ de ProbabilitÚs de Saint-Flour XXXIV-2004
Series: Lecture Notes in Mathematics Vol. 1908
3. Lyons, T.J. & Victoir, N. 2004 Cubature on Wiener Space, Proc. R. Soc.
Lond. A 460,. 169-198.
4. Christian Litterer and Terry Lyons, High order recombination and an
application to cubature on Wiener space, manuscript to appear.