Hinweis: Diese Veranstaltung wird im Wintersemester 2014/15 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.

Stochastic Analysis in winter term 2014/15

Dates:Thursdays, 10:15 to 11:45 in room PR 2.02.01 (lecture hall, 2nd floor) at Parkring 11 in Garching-Hochbrück.
Start: 9th October 2014
Instructor:Prof. Dr. Noam Berger
Prerequisites:Probability Theory
Content:Martingales in continuous time, Brownian motion: construction and properties, Donsker's invariance principle, Stochastic integrals, Ito's formula, stochastic differential equations, Girsanov's theorem

(no material other than a pencil and a brain will be allowed in the exams)

  • 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.



Lecture notes from 2011/12 are available here.

Final exam

Final exam:

1st EXAM: Thu 19.02.15, 13h00-14h30, 101, Interims Hörsaal 1 (5620.01.101).

*** Here you can find the text of the first exam! ***


2nd EXAM: Wed 01.04.15, 15h00-16h30, 102, Interims Hörsaal 2 (5620.01.102).

Post-exam review:Review of the first exam: Tuesday, March the 3rd, in the usual lecture room in Hochbrück (PR 2.02.01, 2nd floor), from 11h00 until 12h30.
Exercise classes:
Dates of classes:

Group 1: Thursdays of even weeks, 12:15 - 13:45, Start: 16th October
Group 2: Thursdays of odd weeks, 08:30 - 10:00, Start: 23rd October
Group 3: Thursdays of odd weeks, 12:30 - 14:00, Start: 23rd October

ATTENTION! The class of the 4th December has been replaced because of the Dies Academicus. New possible dates are December the 3rd, 10h30-12h00, or December the 5th, 12h30-14h00. ̶S̶̶a̶̶m̶̶e̶̶ ̶̶r̶̶o̶̶o̶̶m̶̶.

DOUBLE ATTENTION!! The room for the 3rd, 10h30-12h00, has been changed. The lecture will take place in Room 0.01.04, in the Edeka building. The lecture on the 5th is instead in the usual room. Sorry for the mess!



There will be a Q&A session on Thursday the 12th of February, from 10h30 to 12h00 in the main lecture room. If you want any topic/exercise to be repeated, or you have question of (almost) any kind on the course, send me (Michele) an e-mail beforehand. We will also discuss some exercises from Sheet 8 (no homework there, no online solutions...).


See dates and rooms

Organization of classes:Michele Salvi
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 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.

Please work in a group of two or three on your homework and hand in the homework in English. You can either hand in your homework in the lecture (or in the early group for Group 1) or drop it into the blue box next to Hörsaal 2.02.01 (Parkring 11).

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