The signature of iterated integrals: algebra, analysis and machine learning

The signature of iterated integrals was introduced by Chen in the early part of the 20th century. It maps smooth enough curves \(X: [0,T] \rightarrow \mathbb{R}^d\) into an infinite collection of numbers $$ \int_0^T \int_0^{r_n} \int_0^{r_2} dX^{i_1}_{r_1} .. dX^{i_n}_{r_n}. $$ We will cover The lecture is at 9:00h on Thursdays in A3 02.

Lecture notes (2018-07-10) (will be updated, as we go along)

Lecture 1, 2018-04-12

No lecture on 2018-04-19

Lecture 2, 2018-04-26

Lecture 3, 2018-05-02

No lecture on 2018-05-10

No lecture on 2018-05-17

Lecture 4, 2018-05-24

Lecture 5, 2018-05-30

Lecture 6, 2018-06-07

No lecture on 2018-06-14, because of the Berlin-Oxford meeting

Lecture 7, 2018-06-07

No lecture on 2018-06-21

Lecture 7, 2018-06-28

Lecture 8, 2018-07-05

Lecture 9, 2018-07-12