# Short course on theory of rough paths by Dr. Christian Bayer (Weierstrass Institute)

Rough paths and rough partial differential equations

Terry Lyons' theory of rough paths provides a framework for a deterministic solution theory for rough differential equations, i.e., differential equations driven by a signal which is rougher than 1/2-Hölder. This includes stochastic differential equations of Ito or Stratonovich type. The theory is not restricted to finite dimensional differential equations, but can also be applied to partial differential equations driven by finite or infinite dimensional signals. Moreover, the solution is generally a continuous function of the input (rough) signal in rough path topology. In this mini-course we provide a short, condensed development of the theory of rough paths. We consider the following topics: 1) Motivation and introduction 2) Rough path spaces 3) Integration against rough paths 4) Rough differential equations 5) Rough partial differential equations Literature recommendation: Peter K. Friz and Martin Hairer: A Course on Rough Paths, Springer, 2014. Time and place: First lecture: 13.15-15.00 on Monday, November 16th, undervisningsrom108Niels Henrik Abels hus Second lecture: 8.15-10.00 on Wednesday, November 18th, undervisningsrom107Niels Henrik Abels hus

Published Nov. 9, 2015 11:11 AM
- Last modified Nov. 9, 2015 11:11 AM