Hinweis: Diese Veranstaltung wird im Sommersemester 2013 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 2013



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: 16th 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: Script of the class is available here.
Final exams:

The third exam: December 6th 2013 16:30-18:00.

Location5620.01.102 (Interims Hörsaal 2)

The first exam.

The second exam.

The exam rules (See the link above. Important!) is the same as the first exam.

Dates of classes:

Group 1: Fridays, 10:15 - 11:45 in 03.08.011, Seminarraum (M1/M7) 
Start: 18th April (dates)
Group 2: Thursdays, 12:15 - 13:45 in room 03.10.011, Seminarraum M4/M5/M13 (5610.03.011)
Start: 18th April (dates)
Group 3: Thursdays, 10:15 - 11:45 in room 03.10.011, Seminarraum M4/M5/M13 (5610.03.011)
Start: 18th April (dates)
Group 4: Fridays, 10:15 - 11:45 in room MW 0337, Seminarraum (5503.EG.337)
Start: 19th April (dates)
Group 5: Fridays, 10:15 - 11:45 in room 02.04.011, Seminarraum (M9/M10) (5604.02.011)                                           
Start: 19th April (dates)
Group 6: Fridays, 10:15 - 11:45 in room 02.08.020, Seminarraum (M11/GKAAM) (5608.02.020)                                         
Start: 19th April (dates)

Organisation: Xiaoqin Guo
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 50 % 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 Mr. Xiaoqin Guo.