Time: 17:15-18:00

Location: Mondi 2a

Speaker: Martin Gbur (first year student)

Title: Rough paths and quadratic variation

Abstract: The signature of a path is a sequence, whose n-th term contains n-th order iterated integrals of the path. These iterated integrals of sample paths of stochastic processes arise naturally as the solutions of differential equations driven by those processes, but they also have an intimate connection to the geometry of the path. I will give you an introduction to the theory of rough paths, and describe a relation between the asymptotic behaviour of the signature of Brownian motion and its quadratic variation. Then I will present joint work with H. Boedihardjo done in a summer project, where we extended this connection to a more general class of processes. We also established a connection between the signature of fractional Brownian motion and its Hurst parameter and conjectured an extension to higher dimensions.