Dieses Modul ist Teil einer langfristigen Gesamtlehrplanung für das Masterprogramm, die sicherstellt, dass in allen fünf Gebieten jedes Jahr jeweils mindestens Module im Umfang von 20 LP angeboten werden. Im Rahmen dieser Gesamtlehrplanung wird das Modul in unregelmäßigen Abständen angeboten.
10 Credit points
For information on the duration of the modul, refer to the courses of study in which the module is used.
Non-official translation of the module descriptions. Only the German version is legally binding.
Students master advanced content and methods of the theory of Stochastic Processes, in particular they can independently carry out very complex proofs in this area requiring a higher level of mathematical expertise. They acquire basic tools related to weak convergence on spaces of functions and random walks or in ergodic theory. Concretely:
Students will be introduced to current research questions in the area of Stochastic Processes. They are able to recognise and assess further development opportunities and research goals.
Furthermore, students recognise further-reaching connections to mathematical issues that have already been worked out. They can transfer and apply the knowledge and methods they have learnt so far to deeper mathematical problem areas. Students also expand their mathematical intuition as a result of more intensive study.
In combination with other in-depth modules, they will be able to write their own research papers, e.g. a master's thesis in the field of Stochastic Processes.
In the tutorials, students develop their ability to discuss mathematical topics and thus further prepare themselves for the requirements of the Master's module, in particular for the scientific discussion within the Master's seminar presentation and the defence of their Master's thesis.
Concretisation B:
If necessary, addition of special features
Further teaching content from the area of stochastic processes can be:
I. Weak convergence on spaces of functions and random walks
(1) Weak convergence on spaces of continuous functions
(2) Functional CLT
(3) Skorohod embedding
(4) Convergence of empirical processes
(5) Analysis of boundary-crossing problems for random walks
or
II Ergodic theory and countable Markov chains
(1) Birkhoff-Khinchin theorem and ergodic sequences
(2) Renewal theory
(3) Classification of Markov chains and ergodic theorem
(4) Potential theory of Markov chains
This module prepares the content of a master's thesis.
Solid knowledge of probability theory (24-M-PT-STP)
—
Module structure: 1 SL, 1 bPr 1
| Allocated examiner | Workload | LP2 |
|---|---|---|
|
Teaching staff of the course
Tutorials Stochastic Processes
(exercise)
Regular completion of the exercises, each with a recognisable solution approach, as well as participation in the exercise groups for the module's lecture. As a rule, participation in the exercise group includes presenting solutions to exercises twice after being asked to do so as well as regular contributions to the scientific discussion in the exercise group, for example in the form of comments and questions on the proposed solutions presented. The organiser may replace some of the exercises with face-to-face exercises. |
see above |
see above
|
(electronic) written examination in presence of usually 120 minutes, oral examination in presence or remote of usually 40 minutes, A remote electronic written examination is not permitted.
| Degree programme | Profile | Recommended start 3 | Duration | Mandatory option 4 |
|---|---|---|---|---|
| Mathematical Economics / Master of Science [FsB vom 28.02.2025] | Mathematics | 2. o. 3. | one semester | Compulsory optional subject |
| Mathematical Economics / Master of Science [FsB vom 28.02.2025] | Economics | 2. o. 3. | one semester | Compulsory optional subject |
| Mathematics / Master of Science [FsB vom 28.02.2025] | 2. o. 3. | one semester | Compulsory optional subject |
The system can perform an automatic check for completeness for this module.