Stochastic Analysis


On Thursdays, 10:00 bis 12:00 in room 3.5.06, Hochbrück-Seminarraum 3 (Parkring 35-39; entrance on the right side next to Edeka)

Instructor: Prof. Dr. Nina Gantert
Prerequisites: Probability Theory
Lecture notes of Prof. Gantert's lecture are available here

Martingales in continuous time, Brownian motion: construction and properties, Donsker's invariance principle, Stochastic integrals, Ito's formula, stochastic differential equations, Girsanov's theorem


Ioannis Karatzas and Steven Shreve: Brownian motion and stochastic calculus, Springer, 2007. 

Achim Klenke: Probability Theory, Springer, 2008. (List of typos

Thomas Liggett: Continuous time Markov processes: An introduction, American Mathematical Society, 2010. 

Peter Mörters and Yuval Peres: Brownian motion, Cambridge University Press, 2010. 

Script: Lecture notes are available here. (Last update: June 20)
Final exam:

The final exam takes place on February 27 (2012) from 11:30 - 12:30 in room 5510.EG.001 (MW 0001, Gustav-Niemann-Hörsaal CH).

Remark: You will have the opportunity to look into your corrected exams on March 9 (Friday) between 11:00 and 12:00 in room PR 2.02.30A (Besprechungszimmer - Lehrstuhl für Wahrscheinlichkeitstheorie).

The second exam takes place on April 13 (2012) from 9:00 - 10:00 in room 2.02.01 (Hochbrück-Hörsaal).

Exercise classes:
Dates of classes:

Group A (in English): On Thursdays, 8:30 - 10:00 in room 3.1.08 (Hochbrück-Seminarraum 1). Start: November 3 (Dates)
Group B (in German): On Thursdays, 12:00 - 13:30 in room 3.5.06 (Hochbrück-Seminarraum 3). Start: November 3 (Dates)
Group C (in German): On Thursdays, 16:15 - 17:45 in room 2.01.10 (Hochbrück-Tutorraum 1). Start: October 27 (Dates)

Organization of classes: Michael Kochler
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 achievable 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.

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If you have any questions concerning the exercise classes, please contact Michael Kochler.