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 WS 2013/4
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|
|SS 2021||SS 2020||SS 2014||WS 2013/4|
MA4405 is a semester module in English language at Master’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)|
|180 h||60 h||6 CP|
Content, Learning Outcome and Preconditions
- define Brownian motion and apply basic calculations
involving Brownian motion
- understand fundamental results such as the reflection
principle for Brownian motion, Lévy's Theorem and
Donsker's invariance principle
- understand the basics of stochastic integration
- apply Itô's formula
- understand the basics of stochastic differential equations
- apply change-of-measure techniques.
Courses, Learning and Teaching Methods and Literature
Courses and Schedule
|VO||3||Stochastic Analysis||Bäumler, J. Gantert, N. Tokushige, Y.||
Thu, 08:30–11:30, virtuell
|UE||1||Stochastic Analysis (Exercise Session)||Bäumler, J. Gantert, N. Tokushige, Y.||dates in groups||
Learning and Teaching Methods
The module is offered as lectures with accompanying practice sessions. In the lectures, the contents will be presented in a talk with demonstrative examples, as well as through discussion with the students. The lectures should motivate the students to carry out their own analysis of the themes presented and to independently study the relevant literature. Corresponding to each lecture, practice sessions will be offered, in which exercise sheets and solutions will be available. In this way, students can deepen their understanding of the methods and concepts taught in the lectures and independently check their progress.
P. Mörters, Y. Peres (2010): Brownian Motion, Cambridge University Press, New York / Melbourne / Madrid / Cape Town / Singapore / Sao Paulo / Delhi / Dubai / Tokyo
Description of exams and course work
Students have to know theoretical foundations of Brownian motion, Lévy's Theorem and Donsker's invariance principle. They are able to understand the basics of stochastic integration and stochastic differential equations and can apply Itô's formula.
The exam may be repeated at the end of the semester.