This website is no longer updated.

As of 1.10.2022, the Faculty of Physics has been merged into the TUM School of Natural Sciences with the website For more information read Conversion of Websites.

de | en

Advanced Probability Theory

Module MA2411

This Module is offered by TUM Department of Mathematics.

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.

Basic Information

MA2411 is a semester module in German or English language at Master’s level which is offered once.

This module description is valid from WS 2010/1 to WS 2010/1.

Total workloadContact hoursCredits (ECTS)
150 h 45 h 5 CP

Content, Learning Outcome and Preconditions


- Conditional expectations.
- Martingales: inequalities, convergence theorems, optional stopping theorem.
- Brownian motion.

Learning Outcome

At the end of the module students are able to understand and apply martingale theory and the basic theory of the Brownian motion.


MA1001 Analysis 1, MA1002 Analysis 2, MA2003 Measure and Integration, MA1401 Introduction to Probability Theory, MA2408 Probability Theory

Courses, Learning and Teaching Methods and Literature

Learning and Teaching Methods

Vorlesung, Übung, Übungsaufgaben zum Selbststudium


Semesterapparat, Tafelarbeit, Übungsblätter


Rick Durrett: Probability: Theory and Examples, Duxbury advanced series, third edition, 2005.
Achim Klenke: Probability Theory: A Comprehensive Course, Springer, 2008.

Module Exam

Description of exams and course work


Exam Repetition

The exam may be repeated at the end of the semester.

Top of page