Mon, 21 Feb 2005
15:45
DH 3rd floor SR

Perspectives on the mathematics of the integral of geometric Brownian motion

Professor Michael Schroeder
(University of mannheim)
Abstract

This talk attempts to survey key aspects of the mathematics that has been developed in recent years towards an explicit understanding of the structure of exponential functionals of Brownian motion, starting with work of Yor's in the 1990s

Mon, 21 Feb 2005
14:15
DH 3rd floor SR

Characterisation of paths by their signatures

Dr Nadia Sidorova
(Oxford)
Abstract

It is known that a continuous path of bounded variation

can be reconstructed from a sequence of its iterated integrals (called the signature) in a similar way to a function on the circle being reconstructed from its Fourier coefficients. We study the radius of convergence of the corresponding logarithmic signature for paths in an arbitrary Banach space. This convergence has important consequences for control theory (in particular, it can be used for computing the logarithm of a flow)and the efficiency of numerical approximations to solutions of SDEs. We also discuss the nonlinear structure of the space of logarithmic signatures and the problem of reconstructing a path by its signature.