Probability Theory in summer term 2011

Lecture
Dates:

The lecture has already taken place.

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

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.

Literature:

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

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

Achim Klenke: Wahrscheinlichkeitstheorie,
Springer, 2009

Script:

Lecture notes are available here.

Final exam:
Date:

The exams have already taken place.

Exercise classes:
Dates of classes: The exercise classes have already taken place.
Organization of classes: Christian Bartsch, Mikael Falconnet

 

If you have any questions concerning the exercise classes, please contact Christian Bartsch.