Universität Ulm, Fakultät für Mathematik und Wirtschaftswissenschaften - Abteilung Stochastik

Markov Chains and Monte Carlo Simulation


Mo., 16th October, 15:15-17:15 H7

  Lecturer: Prof. Dr. Volker Schmidt
  Class Teacher (Exercises): Dipl.-Math.oec. Ursa Pantle
  Class Teacher (Tutorial): Sebastian Lück
  Type: Lecture (2 SWS),  Exercise class (1 SWS),  Tutorial class (1 SWS)
MSc Finance: Optional Course in Mathematics (6 CP)
Lectures:Tu, 10-12 c.t., H 7
Exercise Classes:Fr, 8:30-10 s.t., He 220 (alternating)
Tutorial Classes:Fr, 8:30-10 s.t., He 220 (alternating)
  Final Exam:
  Prerequisites: Probability Calculus (required), Statistics (recommended)
Wahrscheinlichkeitsrechnung (Voraussetzung), Statistik I & II (empfohlen)
  Contents: Markov chains represent one of the basic statistical models for sequences of random variables, which exhibit a certain dependence structure. There exist various applications, amongst others, in finance and insurance, but also in life sciences for example. However, it often arises the problem, that the mathematical model becomes so complex that explicit analytic fomulas do not exist. In this case, Markov-Chain-Monte-Carlo-Simulation is used as an auxiliary tool to obtain approximative solution s.
Topics will include:
  • Time-discrete Markov chains with finite state space.
  • Stationarity and Ergodicity.
  • Markov-Chain-Monte-Carlo (MCMC).
  • Reversibility and Coupling.
Printed version of lecture notes now available! Pick up your reserved copy at basic price of EUR 5,-.
  Lecture notes:
  (preliminary version)
  Material from the Tutorial:
  Exercise Sheets:
  Lecture notes:
  (German only)
Probability Calculus, Statistics I and Statistics II
  • E. Behrends
    Introduction to Markov Chains.
    Vieweg, Braunschweig 2000

  • P. Bremaud
    Markov Chains, Gibbs Fields, Monte Carlo Simulation, and Queues
    Springer, New York 1999

  • O. Häggström
    Finite Markov Chains and Algorithmic Applications
    Cambridge University Press, Cambridge 2002

  • U. Krengel
    Einführung in die Wahrscheinlichkeitstheorie und Statistik
    Vieweg, Braunschweig 2002

  • S.I. Resnick
    Adventures in Stochastic Processes
    Birkhäuser, Boston 1992

  • T. Rolski, H. Schmidli, V. Schmidt, J. Teugels
    Stochastic Processes for Insurance and Finance
    Wiley, Chichester 1999

  • G. Winkler
    Image Analysis, Random Fields and Dynamic Monte Carlo Methods
    Springer, Berlin 2003

Last change: 05/09/06, Ursa Pantle.