2318 Stochastische Prozesse
Dr. Paul Eisenberg
  • LV-Typ
  • Semesterstunden
  • Unterrichtssprache
14.09.2020 bis 04.10.2020
Anmeldung über LPIS
Hinweise zur LV
Planpunkt(e) Doktorat/PhD
Wochentag Datum Uhrzeit Raum
Mittwoch 07.10.2020 16:00 - 19:00 D4.0.039
Mittwoch 14.10.2020 16:00 - 19:00 D4.0.039
Mittwoch 21.10.2020 16:00 - 19:00 D4.0.144
Mittwoch 28.10.2020 13:00 - 16:00 D4.0.133
Mittwoch 04.11.2020 16:00 - 19:00 D4.0.144
Mittwoch 11.11.2020 16:00 - 19:00 D4.0.144
Mittwoch 18.11.2020 13:00 - 16:00 D4.0.019

Ablauf der LV bei eingeschränktem Campusbetrieb

In case that only a more limited number of students may come to the campus: Reduced presence during lecture/tutorials and students will be provided by online learning material, e.g. recorded lecture, lecture notes.

If no students are allowed on the campus,then shift to full on-line learning: Recorded lectures, lecture notes, Tutorials will be moved to Teams.

Inhalte der LV

The course deepens the understanding of concepts, methods and tools from stochastic analysis; specifically continuous time Markov chains and Levy processes.

It introduces two main mathematical concepts, namely continuous time Markov chains and Levy processes. Markov chains play a prominent role in financial modelling where they are often used for regime-switching phenomena. Levy processes are a natural generalisation of Brownian motion and many concepts for Brownian motion can be generalised to Levy processes. More importantly, they give a key understanding of semimartingales in general which somewhat locally behave like Levy processes.

This course starts with an outline of its goals. Then, continuous time Markov chains are discussed. We develop transition graphs, transition laws, semigroups and generators for them. Subsequently, we start to deal with Levy processes, discuss its Levy-Ito decomposition and introduce the so-called Levy triplet. The latter is a minimal probabilistic description of the Levy process at hand.

Lernergebnisse (Learning Outcomes)

After completing the course, students will be able to handle continuous time Markov chains and have a basic understanding of Levy processes. This enables the students to read and understand further textbooks on these topics as well as understanding introductions to semimartingales and their characteristics.

Regelung zur Anwesenheit

Full attendance is compulsory. This means that students should attend at least 80% of all lectures, at most one lecture can be missed.


This course is taught as lectures and tutorials with exercise which have to be solved individually by the students. In combination with the lectures, the course exercises will help students to consolidate and expand their understanding of the theoretical and applied methods discussed in the lectures.

Leistung(en) für eine Beurteilung

Course evaluation consists of three parts:

  • Final oral exam of approx. 15 min length (50 per cent)
  • Active participation during classes (26 per cent)
  • 6 Homework assignments (24 per cent)

Empfohlene inhaltliche Vorkenntnisse

Students require prior knowledge on probability theory and preferable knowledge/intuition on conditional expectation.

Zuletzt bearbeitet: 26.06.2020