Information on the lecture Markov Chains (WS 2025/2026)

Lecturer: JProf. Dr. David Criens

Assistant: M. Sc. Dario Kieffer

Date: Wed, 10-12h, SR 226, Hermann-Herder-Str. 10

Exercise class: Thu, 12-14h, SR 232, Ernst-Zermelo-Str. 1

ECTS: 6 points

Language: English

The class of Markov chains is an important class of (discrete-time) stochastic processes that are used frequently to model for example the spread of infections, queuing systems or switches of economic scenarios. Their main characteristic is the Markov property, which roughly means that the future depends on the past only through the current state. In this lecture we provide the mathematical foundation of the theory of Markov chains. In particular, we learn about path properties, such as recurrence and transience, state classifications and discuss convergence to the equilibrium. We also study extensions to continuous time. On the way we discuss applications to biology, queuing systems and resource management. If the time allows, we also take a look at Markov chains with random transition probabilities, so-called random walks in random environment, which is a prominent model in the field of random media.

ILIAS

The lecture notes, exercise sheets, as well as announcements regarding both, the lecture and the exercise class can be found on ILIAS.

Literature

J. R. Norris: Markov Chains, Cambridge University Press, 1997

Prior knowledge

Necessary: Stochastics I

Useful: Analysis III, Probability Theory I

Usable in the following modules:

Wahlpflichtmodul Mathematik (BSc21)
Angewandte Mathematik, Mathematik oder (nach Absprache mit Prüfer:in) Vertiefungsmodul (MSc14)
Elective in Data (MScData24)
Wahlmodul (MSc14)
Mathematische Ergänzung (MEd18)
Wahlmodul im Optionsbereich Individuelle Studiengestaltung (2HfB21)

Consulting hours

Lecturer consultation hours: by appointment
Assistant consultation hours: by appointment