Universität Wien

250042 VO Stochastic Processes (2025W)

6.00 ECTS (4.00 SWS), SPL 25 - Mathematik
Moodle
Tu 16.12. 16:45-18:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß

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Details

Language: English

Examination dates

Lecturers

Classes (iCal) - next class is marked with N

  • Wednesday 01.10. 16:45 - 18:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Tuesday 07.10. 16:45 - 18:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Wednesday 08.10. 16:45 - 18:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Tuesday 14.10. 16:45 - 18:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Wednesday 15.10. 16:45 - 18:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Tuesday 21.10. 16:45 - 18:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Wednesday 22.10. 16:45 - 18:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Tuesday 28.10. 16:45 - 18:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Wednesday 29.10. 16:45 - 18:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Tuesday 04.11. 16:45 - 18:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Wednesday 05.11. 16:45 - 18:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Tuesday 11.11. 16:45 - 18:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Wednesday 12.11. 16:45 - 18:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Tuesday 18.11. 16:45 - 18:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Wednesday 19.11. 16:45 - 18:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Tuesday 25.11. 16:45 - 18:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Wednesday 26.11. 16:45 - 18:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Tuesday 02.12. 16:45 - 18:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Wednesday 03.12. 16:45 - 18:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Tuesday 09.12. 16:45 - 18:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Wednesday 10.12. 16:45 - 18:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Wednesday 17.12. 16:45 - 18:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Wednesday 07.01. 16:45 - 18:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Tuesday 13.01. 16:45 - 18:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Wednesday 14.01. 16:45 - 18:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Tuesday 20.01. 16:45 - 18:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Wednesday 21.01. 16:45 - 18:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Tuesday 27.01. 16:45 - 18:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Wednesday 28.01. 16:45 - 18:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß

Information

Aims, contents and method of the course

Stochastic processes describe the evolution of systems subject to randomness.
The simplest example of such systems are Markov chains, in which only information about the present state is retained for the future evolution.
Although these are simple to describe and arise in a large number of applications, there is a surprisingly rich theory describing the behaviour of such systems in the large time limit.
After discussing Markov chains in discrete time and discrete space, we will move on to the notion of martingale. This
fundamental concept plays the same role for stochastic processes that "constants of motion'' play in physics.

Assessment and permitted materials

Written exam

Minimum requirements and assessment criteria

50% at written exam required for pass grade.

Examination topics

Markov chains: recurrence, transience, invariant measure, convergence to equilibrium.
Martinagles: stopping times, optional stopping, convergence theorem.

Reading list

Lecture notes for the course are available at the following link:
https://www.dropbox.com/scl/fi/hczvfjnysquhn72mtcrt2/StochasticProcesses.pdf?rlkey=hi0ljol5l1hwwqazimw3tr7dw&dl=0
(The file at this link will be updated as needed, but the link should remain the same).

Otherwise, an excellent book for this course is "Markov chains", by James Norris (Cambridge University Press).

Association in the course directory

MSTP; MBIP; ML1; MEL

Last modified: Tu 09.12.2025 09:47