This module handbook serves to describe contents, learning outcome, methods and examination type as well as linking to current dates for courses and module examination in the respective sections.
Module version of SS 2019
There are historic module descriptions of this module. A module description is valid until replaced by a newer one.
Whether the module’s courses are offered during a specific semester is listed in the section Courses, Learning and Teaching Methods and Literature below.
|available module versions|
|WS 2021/2||SS 2020||SS 2019||WS 2011/2||SS 2011|
MA2404 is a semester module in German language at Bachelor’s level which is offered in winter semester.
This Module is included in the following catalogues within the study programs in physics.
- Specialization Modules in Elite-Master Program Theoretical and Mathematical Physics (TMP)
|Total workload||Contact hours||Credits (ECTS)|
|150 h||45 h||5 CP|
Content, Learning Outcome and Preconditions
2. Filtration, stopping times, strong Markov property, hitting times.
3. Communicating classes, closed sets, irreducibility, recurrence and transience, return times, absorption, aperiodicity.
4. Invariant measure and stationary distribtution, convergence theorem, ergodic theorem for Markov chains, positive and null recurrence.
5. Law of large numbers, time reversal, detailed balance. Examples: e.g. random walk, ruin problem, birth and death process, Galton Watson branching process, queuing model, Ehrenfest model.
Courses, Learning and Teaching Methods and Literature
Courses and Schedule
|UE||1||Markov Chains (Exercise Session)|
Learning and Teaching Methods
- Norris, J.R. (1999) Markov Chains. Cambridge University Press.
- Wolfgang Woess, Denumerable Markov chains, European Mathematical Society, 2009.
Description of exams and course work
The exam may be repeated at the end of the semester.
Current exam dates
Currently TUMonline lists the following exam dates. In addition to the general information above please refer to the current information given during the course.