Main content
Stochastical Analysis
(dt. Stochastische Analysis)
Level, degree of commitment | Specialization module, compulsory elective module |
Forms of teaching and learning, workload |
Lecture (4 SWS), recitation class (2 SWS), 270 hours (90 h attendance, 180 h private study) |
Credit points, formal requirements |
9 CP Course requirement(s): Successful completion of at least 50 percent of the points from the weekly exercises. Examination type: Written or oral examination (individual examination) |
Language, Grading |
English,The grading is done with 0 to 15 points according to the examination regulations for the degree program M.Sc. Business Mathematics. |
Duration, frequency |
One semester, Regularly alternating with other specialization modules |
Person in charge of the module's outline | Prof. Dr. Hajo Holzmann |
Contents
We introduce stochastic integration and applications. Different topics cover, for instance, stochastic differential equations, jump processes and applications in financial mathematics.
Qualification Goals
The students
- Have gained an insight into the research field of stochastic analysis,
- know basic structures and techniques of stochastic analysis,
- know selected applications of stochastic analysis,
- have deepened mathematical working methods (developing mathematical intuition and its formal justification, abstraction, proof),
- have improved their oral communication skills in exercises by practicing free speech in front of an audience and in discussion.
Prerequisites
None. The competences taught in the following modules are recommended: either Foundations of Mathematics and Linear Algebra I and Linear Algebra II or Basic Linear Algebra, either Analysis I and Analysis II or Basic Real Analysis, Probability Theory.
Applicability
The module can be attended at FB12 in study program(s)
- B.Sc. Mathematics
- B.Sc. Business Mathematics
- M.Sc. Data Science
- M.Sc. Computer Science
- M.Sc. Mathematics
- M.Sc. Business Mathematics
- LAaG Mathematics
When studying M.Sc. Business Mathematics, this module can be attended in the study area Free Compulsory Elective Modules.
The module can also be used in other study programs (export module).
Recommended Reading
- Oksendal, B., „Stochastic Differential Equations: An Introduction with Applications“. Springer-Verlag Berlin 1998
- Karatzas, I., Shreve, S., „Brownian Motion and Stochastic Calculus“. Springer-Verlag Berlin 1991
- Protter, P., „Stochastic Integration and Differential Equations: A New Approach“. Springer-Verlag Berlin 2003
- Revuz, D., Yor, M., „Continuous Martingales and Brownian Motion“. Springer 2005
Please note:
This page describes a module according to the latest valid module guide in Winter semester 2023/24. Most rules valid for a module are not covered by the examination regulations and can therefore be updated on a semesterly basis. The following versions are available in the online module guide:
- Winter 2016/17
- Summer 2018
- Winter 2018/19
- Winter 2019/20
- Winter 2020/21
- Summer 2021
- Winter 2021/22
- Winter 2022/23
- Winter 2023/24
The module guide contains all modules, independent of the current event offer. Please compare the current course catalogue in Marvin.
The information in this online module guide was created automatically. Legally binding is only the information in the examination regulations (Prüfungsordnung). If you notice any discrepancies or errors, we would be grateful for any advice.