We first give an introduction and some motivation to rough path theory and its application to differential equations driven by fractional Brownian motion. Then we briefly review stochastic calculus according to Itô, with a language which can be easily adapted to our future considerations.

The slides, part 1, can be downloaded here.

We show that differential calculus with respect to fractional Brownian motion with Hurst parameter H different from 1/2 cannot be handled thanks to martingale type arguments. We then treat the case H>1/2 by means of Young integrals. This integration theory will be introduced with two different methods: (i) An elementary way based on Riemann sums. (ii) By means of algebraic integration techniques, which will be at the heart of our future discussions and can be introduced in an elementary manner in this context.

The slides, part 2, can be downloaded here.

We treat the case of level 2 rough paths, an apply our results to differential equations driven by a fractional Brownian motion with Hurst parameter 1/3<H<1/2. We will try to give some insight on technical details. According to the time being left, we will then introduce Malliavin calculus tools applied to rough differential equations.

The slides, part 3, can be downloaded here.

The slides, part 4, can be downloaded here.

Tuesday 16 July at13:00 accompanied with wine & cheese in Vandrehallen.

Deadline for registration: July 1, 2016.

Professor Mark Podolskij, Department of Mathematics, Aarhus University. E-mail: mpodolskij@math.au.dk

For further information please contact Oddbjørg Wethelund, Administrative Officer. Tel +45 87155791. E-mail: oddbjorg@math.au.dk