Department Mathematik
print


Navigationspfad


Inhaltsbereich

Stochastic Processes WS 19/20

Registration

Please register for the course here.

News

[31.03.20] The original intention was to schedule oral retake exams for “Stochastic Processes” during the week of April 20 (first week of term). Currently, the university buildings are closed down, and conventional exams therefore impossible. It is currently not clear how the situation is developing, it might be that we have to shift the exams to a later date, or that we have to use telecommunication software. Therefore, we adopt the following procedure: Those that are willing to take the retake exam should register by email to me, Thomas Beekenkamp, by the 7th of April. You will then be notified by email about the date and the circumstances of the exam at a later time (at least one week before the exam is to be scheduled). If you already passed the course in the regular exam, you will not be able to partake in the retake exam to improve your grade (imposed by the study regulations of the master programs).

[03.02.20] The schedule for the exam can be found here.

[03.02.20] There will be no lecture on Monday, February 3rd.

[30.01.20] The oral exam will take place on Wednesday, Thursday and Friday, the 12th, 13th and 14th of February. On Wednesday we have slots in the afternoon, and on Thursday and Friday we have slots in the morning and afternoon. If you want to partake in the exam, please send me an email with your preferred slot(s) by Monday, February 3rd.

[16.12.19] Please hand in the homework of sheet 10 before Tuesday, January 7th, 10:00, so we can still discuss it on the same day.

[25.10.19] I made some clarifications to exercise H2 of sheet 2.

[30.09.19] Welcome to the website of the stochastic processes course. The first lecture will be on Monday, October 14th.


Times and locations

Lecture: Monday 12:00-14:00 c.t. B 0004 Markus Heydenreich
Thursday 14:00-16:00 c.t. B 0004
Exercise Class: Tuesday 14:00-16:00 c.t. B 0004 Thomas Beekenkamp
Office hour: Wednesday, 15:00-16:00
Please check the news section for cancellations and room changes.

Exercises

Sheets:
SheetDue on:Solutions
Sheet 1 Monday, October 21stSolutions
Sheet 2 Monday, October 28thSolutions
Sheet 3 Monday, November 4thSolutions
Sheet 4 Monday, November 11thSolutions
Sheet 5 Monday, November 18thSolutions
Sheet 6 Monday, November 25thSolutions
Sheet 7 Monday, December 2ndSolutions
Sheet 8 Monday, December 9thSolutions
Sheet 9 Monday, December 16thSolutions
Sheet 10 Tuesday, January 7thSolutions
Sheet 11 Tuesday, January 14thSolutions
Sheet 12 Tuesday, January 21stSolutions
Sheet 13 Tuesday, January 28stSolutions
Sheet 14 Tuesday, February 3rdSolutions
Sheet 15 Solutions
Please hand in your solutions on Monday before 14:00, either in the lecture, in person or in the dropbox 56. I will discuss the handed in solutions individually in the following exercise class.

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

Literature

The course follows the presentation in
  • 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. Mörters, 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
  • R. Durrett, Probability. Theory and Examples, 4th edition, Cambridge University Press 2010. Link
    - Contains all the basics in probability theory

Retake exam

The original intention was to schedule oral retake exams for “Stochastic Processes” during the week of April 20 (first week of term). Currently, the university buildings are closed down, and conventional exams therefore impossible. It is currently not clear how the situation is developing, it might be that we have to shift the exams to a later date, or that we have to use telecommunication software. Therefore, we adopt the following procedure: Those that are willing to take the retake exam should register by email to me, Thomas Beekenkamp, by the 7th of April. You will then be notified by email about the date and the circumstances of the exam at a later time (at least one week before the exam is to be scheduled). If you already passed the course in the regular exam, you will not be able to partake in the retake exam to improve your grade (imposed by the study regulations of the master programs).