Stochastic Processes

Prof. Anton Wakolbinger

Sommersemester 2010

Final (written) exam (Abschlussklausur)
on Friday, July 16, 2010, 12:30
Hörsaal H II (not H 2) .

Vorlesung (Course): 4-stündig
Dienstag, Freitag 12:15-14:00, H2, Hörsaalgebäude Gräfstr.

Übungen (Tutorial): 2-stündig.


For those who did not pass or could not take part in the final exam, a second written exam (Zweitklausur) will take place on Monday, October 11, 2010, 10:15-11:45, in Hörsaal H I.

Final exam           Scores

For a look into your exam achievements (and the correct solutions), Christian Böinghoff (Room 705) will be availablle on Tue July 27, 10:00-11:30 , Thu July 28, 14:00-16:00, and Wed August 4, 10:00- 11:30.


This course is an introduction to concepts and applications of stochastic processes. It is designed for students of mathematics and finance. Also students from other disciplines (like computer science, physics or biology) are welcome. The course assumes basic knowledge of probability theory, as taught in the course ''Elementare Stochastik'', or provided by my textbook with Götz Kersting, Elementare Stochastik, Birkhäuser 2008

The contents of the course are:

  • Conditional expectation and Martingales;
  • Markov chains in discrete and continuous time;
  • Poisson processes and their relatives;
  • Brownian motion and stochastic calculus.

    The course language will be English or German, depending on preferences of the students.


    The course will be accompanied by a tutorial (2 hours per week), which will take place in 3 groups:

    Tuesday 10-12 (starting April 13, 2010), Room 310, Tutor: Christian Böinghoff,
    Thursday 10-12 (starting April 15, 2010), Room 711 gr, Tutor: Ute Lenz (Offices: Room 312, Robert-Mayer-Str. 6, and Room 01.304, Campus Riedberg),
    Friday 10-12 (starting April 16, 2010), Room 711 kl, Tutor: Ute Lenz.

    Exercises and problems will be provided, and their solutions will be discussed in the tutorials. Participation in a tutorial is an indispensable complement to the course and helps to prepare for the written exam.

    For all students except those in teacher trainig (Lehramtsstudierende), in addition to the score of the final written exam it is possible to earn up to 10 bonus points by participating continuously and successfully in the tutorial. This means: to hand in the correct solutions to at least 50% of the exercises, to present at least two of them on the blackboard and to be prepared to take part in discussions. The same criterion applies for obtaining an ''unbenoteten Übungsschein" (ungraded certificate) in the old program "Diplomstudiengang Mathematik".

    Because the ZPL (Zentrales Prüfungsamt für die Lehrämter) does not accept any flexible bonus point regulation, students in teacher training (Lehramtsstudierende) will get a rigid amount of 5 bonus points. Nonetheless, also these students are cordially invited to take actively part in (and benefit from) the tutorials.

    The assignment are handed out in the course on Tuesday, the written solutions should be handed in at the beginning of the course on the Friday of the subsequent week.

    Assignments and handouts for download:

    Assignments 1 2 3 4 5 6 7 8 9 10 11

    Digest: 1 2

    Handouts: 1 2 3


    Bachelor students have to pass a "Modulteilprüfung". A positive grade can be achieved by obtaining at least 50 from a total of 110 points, with up to 10 points from the Tutorial and up to 100 points from the

    final (written) exam
    on Friday, July 16, 2010, 12:30-14:00
    Hörsaal H II (not H 2) .

    During the exam no support is allowed except up to two (A4-) pages hand-written notes.

    All students who want to participate in the July 16 exam: please (informally) register here till Tuesday July 13.

    Recommended Literature:

  • Grimmet, Geoffrey R., Stirzaker, David R., Probability and Random Processes, 3rd ed., Oxford University Press, 2001;
  • Klenke, Achim, Wahrscheinlichkeitstheorie, Springer 2006. English translation: Probability Theory: A Comprehensive Course. Universitext, Springer 2007.
  • Norris, James, Markov chains, Cambridge University Press, 1997.
  • Williams, David, Probability with martingales, Cambridge University Press, 1991.
  • Kallenberg, Olav, Foundations of Modern Probability, Springer, 2nd ed., 2002.
  • Wakolbinger, Anton; Course notes "Stochastic processes" SoSe 2004.

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