Module 24-M-PT-STP Stochastic Processes

Faculty

Person responsible for module

Regular cycle (beginning)

Every summer semester

Credit points and duration

10 Credit points

For information on the duration of the modul, refer to the courses of study in which the module is used.

Competencies

Non-official translation of the module descriptions. Only the German version is legally binding.

Students master the basic contents and methods of the theory of Stochastic Processes, in particular they can independently carry out complex proofs in this area requiring a high level of mathematical expertise. Students are able to model complex relationships using probabilistic structures as a basis for applications and to analyse these probabilistic structures mathematically, i.e. concretely:

  • Students are able to construct conditional expectations in general and apply them to various application contexts.
  • Students are able to prove the existence of discrete and continuous-time stochastic processes, in particular discrete-time Markov chains and martingales.
  • Students are able to construct Brownian motion in various ways and prove essential properties of Brownian evaluation.
  • Students are able to analyse stochastic processes, in particular the Brownian motion using martingale theory.

Furthermore, the students recognise further-reaching connections to mathematical facts already acquired. 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 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.

Content of teaching

The following basic content of teaching from the field of probability theory is mandatory:

  • Construction of conditional expectation and applications
  • Markov chains and processes
  • Discrete-time martingale theory
  • Time-continuous stochastic processes
  • Brownian motion: various constructions, path properties and finite dimensional distributions,

In addition, the following content of teaching can be covered, for example:

  • Poisson processes
  • Ergodic theory
  • Time-Continuous martingales

Recommended previous knowledge

Basic knowledge of probability theory (such as in module 24-B-EW)

Necessary requirements

Explanation regarding the elements of the module

Module structure: 1 SL, 1 bPr 1

Courses

Lecture Stochastic Processes
Type lecture
Regular cycle SoSe
Workload5 60 h (60 + 0)
LP 2 [Pr]
Tutorials Stochastic Processes
Type exercise
Regular cycle SoSe
Workload5 90 h (30 + 60)
LP 3 [SL]

Study requirements

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

Examinations

e-written examination o. written examination o. e-oral examination o. oral examination
Allocated examiner Teaching staff of the course Lecture Stochastic Processes (lecture)
Weighting 1
Workload 150h
LP2 5

(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.

The module is used in these degree programmes:

Degree programme Profile Recom­mended start 3 Duration Manda­tory option 4
Mathematical Economics / Master of Science [FsB vom 28.02.2025] Mathematics 1. o. 2. o. 3. one semester Compul­sory optional subject
Mathematical Economics / Master of Science [FsB vom 28.02.2025] Economics 1. o. 2. o. 3. one semester Compul­sory optional subject
Mathematics / Master of Science [FsB vom 28.02.2025] 1. o. 2. o. 3. one semester Compul­sory optional subject

Automatic check for completeness

The system can perform an automatic check for completeness for this module.


Legend

1
The module structure displays the required number of study requirements and examinations.
2
LP is the short form for credit points.
3
The figures in this column are the specialist semesters in which it is recommended to start the module. Depending on the individual study schedule, entirely different courses of study are possible and advisable.
4
Explanations on mandatory option: "Obligation" means: This module is mandatory for the course of the studies; "Optional obligation" means: This module belongs to a number of modules available for selection under certain circumstances. This is more precisely regulated by the "Subject-related regulations" (see navigation).
5
Workload (contact time + self-study)
SoSe
Summer semester
WiSe
Winter semester
SL
Study requirement
Pr
Examination
bPr
Number of examinations with grades
uPr
Number of examinations without grades
This academic achievement can be reported and recognised.