Information on the Lecture Stochastics III (SS 2025)

Assistent: Samuel Adeosun

Lecture: Wed, 14-16, HS II, Albertstr. 23b, Thu, 10-12, SR 404, Ernst-Zermelo-Str. 1

Exercise: 2-hour, date to be determined

Language: English

Current

You need to achieve at least 50% of the possible points on the exercise sheets and present your solutions in the tutorial at least twice in order to receive the Studienleistung.

Content

This lecture builds the foundation of one of the key areas of probability theory: stochastic analysis. We start with a rigorous construction of the It^o integral that integrates against a Brownian motion (or, more generally, a continuous local martingale). In this connection, we learn about It^o's celebrated formula, Girsanov’s theorem, representation theorems for continuous local martingales and about the exciting theory of local times. Then, we discuss the relation of Brownian motion and Dirichlet problems. In the final part of the lecture, we study stochastic differential equations, which provide a rich class of stochastic models that are of interest in many areas of applied probability theory, such as mathematical finance, physics or biology. We discuss the main existence and uniqueness results, the connection to the martingale problem of Stroock-Varadhan and the important Yamada-Watanabe theory.

Lecture script

The script will be published on Ilias.

Exercise sheets

The exercise sheets will be published on Ilias.

Exercise groups

The time of the exercise group will be determined in the first lecture.

Literature

Necessary knowledge

Wahrscheinlichkeitstheorie I und II (Stochastische Prozesse)

Usability

Wahlmodul im Optionsbereich (2HfB21)
Wahlpflichtmodul Mathematik (BSc21)
Angewandte Mathematik (MSc14)
Mathematik (MSc14)
Vertiefungsmodul (MSc14)
Wahlmodul (MSc14)
Advanced Lecture in Stochastics (MScData24)
Elective in Data (MScData24)

Consultation hour

Lecturer by arrangement
Assistent by arrangement