Department Mathematik



Stochastic Processes WS 17/18


[16.02.18] There is news about the retake exam. Check the exam section!

[02.02.18] We changed exercise H1 a) and H2 of sheet 14 slightly.

[08.01.18] There is news about the exam. Check the exam section!

[21.12.17] Here is a note on H2 of sheet 5. In the exercise class it was assumed that the process on sheet 2 converged to Brownian bridge in distribution, however on we only proved this for the finite dimensional distributions. This note now gives the proof assuming only the convergence of the finite diminensional distributions.

[01.12.17] In the week of 11-17 December the exercise class and the Thursday lecture will be swapped.

[01.12.17] We changed exercise H4 of sheet 7 to be somewhat easier and added a hint.

[09.11.17] There will be no lecture on Thursday, the 16th of November.

[09.11.17] Exercise H2 of sheet 4 has been formulated more precisely.

[09.10.17] There will be a lecture instead of an exercise class on Tuesday in the first week. (17th of October)

Times and locations

Lecture: Monday 14:10-15:50 B004 Christian Hirsch
Thursday 14:15-16:00 B004
Exercise Class: Tuesday 14:15-16:00 B004 Thomas Beekenkamp
Please check the news section for cancellations and room changes.


Please register for the course here.

Exercises and Homework

Due on Solutions
Sheet 1 Tuesday, October 24th Solutions
Sheet 2 Monday, October 30th Solutions
Sheet 3 Tuesday, November 7th Solutions
Sheet 4 Tuesday, November 14th Solutions
Sheet 5 Tuesday, November 21st Solutions
Sheet 6 Tuesday, November 28th Solutions
Sheet 7 Tuesday, December 5th Solutions
Sheet 8 Thursday, December 14th Solutions
Sheet 9 Tuesday, December 19th Solutions
Sheet 10 Tuesday, January 9th Solutions
Sheet 11 Tuesday, January 16th Solutions
Sheet 12 Tuesday, January 23rd Solutions
Sheet 13 Tuesday, January 30th
Sheet 14 Tuesday, February 6th

The exercise sheets are posted every Tuesday, the homework will be due on the next Tuesday at 14:00. Please put your homework in homework box 56 on the first floor, or hand it in during the exercise class.
You can get a bonus for your grade, the height of which depends on the amount of points obtained from the homework exercises, with thresholds at 50% and 75% of the total amount of points. To keep track of your points it is necessary that you are registered for the course. The homework is to be handed in individually, but working together is strongly encouraged.
The homework will be graded by Florian Ingerl, he can be reached at imelflorianingerl [AT] gmail [DOT] com. It will be handed back in the exercise class in the next week.

Course Outline

The following topics will be treated in the course:
  1. Basic Notions
  2. Brownian motion
  3. Markov chains
  4. Feller processes
  5. Interacting particle systems
  6. Poisson point processes


The main book for this course is
  • T.M. Liggett, Continuous Time Markov Processes, AMS 2010.
The following is a list of other relevant literature.
  • L.B. Koralov and Ya. Sinai, Theory of Probability and Random Processes, 2nd edition, Springer 2010.
    - An alternative presentation of the material
  • A. Klenke, Probability Theory, Springer 2014.
    - An even different presentation of the material, also available in German
  • P. M├Ârters, Y. Peres, Brownian Motion, Cambridge University Press 2010. Link
    - Specifically for the chapter on Brownian motion
  • D.A. Levin, Y. Peres, E.L. Wilmer, Markov Chains and Mixing Times, AMS 2009. Link
    - Specifically for the chapter on Markov chains
  • G. Last and M. Penrose, Lectures on the Poisson Process, 2017. Link
    - Lecture notes on Poisson processes and point processes
  • R. Durrett, Probability. Theory and Examples, 4th edition, Cambridge University Press 2010. Link
    - Contains all the basics in probability theory


The oral exam took place on the 14th, 15th and 16th of February.

The retake exam took place on the 12th and 13th of March.