Main content

German original

Probability Theory
(dt. Wahrscheinlichkeitstheorie)

Level, degree of commitment in original study programme Advanced 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
Translation missing. German original:
Studienleistung: Erreichen von mindestens 50 Prozent der Punkte aus den wöchentlich zu bearbeitenden Übungsaufgaben.
Prüfungsleistung: Klausur oder mündliche Prüfung
Language,
Grading
German,
The grading is done with 0 to 15 points according to the examination regulations for study course M.Sc. Business Mathematics.
Original study programme M.Sc. Wirtschaftsmathematik / Mathematische Vertiefungs- und Praxismodule
Duration,
frequency
One semester,
each winter semester
Person in charge of the module's outline Prof. Dr. Hajo Holzmann

Contents

The basic concepts of probability theory, based on measure and integration theory, are discussed, in particular

  • General probability spaces, random variables
  • Independence, laws of large numbers
  • weak convergence, characteristic functions and central limit theorem
  • conditional expectations, conditional distributions, martingales
  • stochastic processes, in particular Brownian motion


Qualification Goals

The students shall

  • learn the basics of probability theory in a mathematically rigorous way, based on measure theory,
  • practice mathematical methods (development of mathematical intuition and its formal justification, training of the ability to abstract, proof methods),
  • improve their oral communication skills in the recitation classes by practicing free speech in front of an audience and during discussion.

Prerequisites

Translation is missing. Here is the German original:

Keine. Empfohlen werden die Kompetenzen, die in den Basismodulen und in den Aufbaumodulen Maß- und Integrationstheorie und Elementare Stochastik vermittelt werden.


Recommended Reading

  • Bauer, H., „Wahrscheinlichkeitstheorie“, de Gruyter 2004.
  • Billingsley, P., „Probability and Measure“, John Wiley & Sons 1995
  • Durrett, R., „Probability Theory and Examples“, Wadsworth & Brooks 1991
  • Klenke, A., „Wahrscheinlichkeitstheorie“, Springer 2008



Please note:

This page describes a module according to the latest valid module guide in Wintersemester 2018/19. 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:

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.