Dr. Joscha Diehl (TU Berlin)

Title: Rough path theory: a quick overview and some applications

Abstract: Differential equations of the form dY = f(Y) dX are covered by classical theory in the case where X is a smooth path. Rough path theory treats such equations when the driving signal X is very irregular in time, e.g. only Hölder continuous for some exponent larger then zero. It turns out that in general the information given by the path itself is not sufficient to build a satisfying theory. The missing piece is some kind of 'higher order' process, which can be thought of as encoding iterated integrals of the path against itself. I will sketch the main ideas of the theory, using an approach that only requires knowledge of undergraduate mathematics.