Course description to "Rough path theory"

Rough path theory, whose foundation was laid by Terry Lions in the 1990?s, has proved to be a very useful and innovative tool in the analysis of stochastic differential equations, stochastic partial differential equations and in applications to statistics, financial data analysis or machine learning.

Rough path theory, which aims at "removing" probability from stochastic systems to the degree possible, enables e.g. the analysis of solutions to stochastic (partial) differential equations in a deterministic way, that is path by path.

This theory, which has links to other branches of mathematics (e.g. Malliavin calculus or Dirichlet forms), provides non-probabilistic techniques with simplified proofs of crucial results in stochastic analysis and their generalizations (e.g. Wong-Zakai theorem or limit theorems of stochastic flows).

The course gives a basic introduction to rough path analysis with applications to stochastic (partial) differential equations, finance and- if time permits- to the theory of regularity structures.