Lecture Summer Term 2015

Markov Chains

Lecturer:
Alexander Lindner
Class Teacher:
Abdulkahar Alkadour
Type:
  • Bachelor Mathematik (optional)
  • Bachelor Wirtschaftsmathematik (optional)
  • Master of Finance (optional)
News:The room of the lecture has changed from He/120 to He/E20 starting from May 7!

Time and Venue:

  • Lecture: Thursday, 12:15-14:00, He18/E20.
  • First Lecture: 16th of April.
  • Exercise Class: every second Friday, 8:30-10:00, He18/E20.
  • Dates of exercise classes: April 24, May 8, May 22, June 5, June 19, July 3, July 17.
  • Solutions of the first exercise sheet to be handed in by: 23rd of April.

Final Exam:

The form of the exam will be determined in the first lecture of the summer term.

Prerequisites:

Analysis I+II, Linear Algebra I+II, Stochastik I.

Contents:

Markov chains in discrete and continuous time with countable state space, in particular:

  • Definition and elementary properties, examples
  • stopping times and strong Markov property
  • recurrence and transience
  • invariant distributions and limit distributions
  • classification of states
  • the generator in continuous time
Literature:
 
  • J.R. Norris, Markov Chains, Cambridge Univ. Press, 1997.
  • G.R. Grimmet and D.R. Stirzaker, Probability and Random Processes, Oxford Science Publications, 1982.
  • S.I. Resnick, Adventures in Stochastic Processes, Birkhäuser, 1992.
  • U. Krengel, Einführung in die Wahrscheinlichkeitstheorie und Statistik, Vieweg, 1988.
Lecture notes:
Problem sheets: