Universität Ulm, Fakultät für Mathematik und Wirtschaftswissenschaften - Abteilung Stochastik

Markov Chains and Monte Carlo Simulation

TIME AND ROOM FOR THE FINAL CHANGED TO

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)
Schedule:
 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)
HTML, PDF
Material from the Tutorial:
Exercise Sheets:
Lecture notes:
(German only)
Probability Calculus, Statistics I and Statistics II
Literature:
• 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