Introduction to Rough Path Theory

Abstract. Rough path theory was introduced by T. Lyons for the study of controlled system of equations driven by irregular paths. The theory extends Young's calculus to paths of arbitrarily low regularity and can be applied to sample paths of random processes like Brownian motion. Such a development allows one to understand Ito calculus and stochastic differential equations in a deterministic setting and comes with many diverse applications. The theory can well be adapted similarly to study stochastic partial differential equations. The fundamentals were based by M. Hairer in the theory of Regularity structures. It then allows one do give meaning to various ill posed SPDEs like Kardar-Parisi-Zhang (KPZ) equation.

The talk intends to give an introduction to the idea and techniques involved behind Rough path theory.