Hinweis: Diese Veranstaltung wird im Sommersemester 2014 in englischer Sprache durchgeführt. Das betrifft insbesondere die Vorlesung sowie die Hausaufgaben. Aus diesem Grund stellen wir fast alle Informationen nur in englischer Sprache zur Verfügung.

Probability Theory im Sommersemester 2014


Tuesdays, 08:30 to 10:00 in room Hochbrück Hörsaal 2 (8102.EG.117) at Parkring 35 (QUANTUM-entrance to the left of EDEKA) in Garching-Hochbrück.

Fridays, 08:15 to 09:45 in room 00.02.001, MI Hörsaal 1 (5602.EG.001) at Boltzmannstr. 3 at FMI-Building at Garching Forschungszentrum.

Start: 8th April 2013 (dates)

Instructor:Prof. Dr. Noam Berger
Prerequisites:Measure and integration theory
Lecture notes of Prof. Lasser's lecture are available here. (in German)

Based on measure and integration theory, in this course the fundamental concepts of probability theory are presented. Of central importance are the different types of convergence, the concept of stochastic independence, and conditional expectations. In addition, the course will deal with the Radon-Nikodym theorem, product spaces and the construction of stochastic processes. For sequences of independent random variables, laws of large numbers and the central limit theorem will be proved. As an important generalization of partial sums of independent random variables, martingales will be introduced and on this basis we will investigate stopping times and prove the martingale convergence theorem.


Rick Durrett: Probability: Theory and Examples,
Cambridge University Press, 2010

Allan Gut: Probability: A Graduate Course,
Springer, 2009

Achim Klenke: Wahrscheinlichkeitstheorie,
Springer, 2009

Script:Here. The script will be regularly updated (Latest Version: 8th of July).
Final exams:

There are no additional materials allowed at the exams.

First exam: Fr 11.7.14 from 8:15 to 9:45 in 5602.EG.001 (00.02.001, MI Hörsaal 1).

First exam review: Fr 18.7.14 from 10:30 to 12:30 in 2.02.01, Hochbrück-Hörsaal (8101.02.201).

Second exam: We 24.9.14 from 15:00 to 16:30 in 102 (5620.01.102 Interims Hörsaal 2).

Second exam review: Mo 6.10.14 from 11:00 to 13:00 in Garching Hochbück 2.02.32. If it is not possible for you to come in that time-frame because of the lectures, send us an email to take an appointment.

Dates of classes:Exercise classes are over. All dates and rooms of previous tutorial classes can be found here.

Repetition and Questions: The repetition and question session for the second exam will take place on Monday, 15th of September, at 2pm in room 2.02.01 (Hochbrück, Parkring 11)

Philipp wrote a nice summary of properties of conditional expectation that you can find here.


Organisation:Michele Salvi and Katja Miller
Bonus system:Your homework will be corrected and rated with points. Through the continuous participation in the exercise course you can receive a bonus on your exam grade. If you achieve at least 60 % of all points, you will get a bonus of one grade level on the grade of your exam if passed (i.e., 1.7 becomes 1.3, 2.3 becomes 2.0, 3.0 becomes 2.7, etc.). Improving the grade 1.0 or failed exams is not possible. This bonus counts only for the two exams corresponding to this lecture.


If you have any questions concerning the exercise classes, please contact Michele Salvi or Katja Miller.