Lecturer
Prof. Dr. Volker Schmidt

Exercises
Dipl.-Math. oec. Florian Timmermann

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Time and place

Lectures
Tuesday, 10:00 - 12:00 (room E20 in He18)

Exercise session and tutorial
Friday, 10:00 - 12:00 Uhr (room E60 in He18)

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Type

2 hours lecture + 1 hour exercises + 1 hour tutorial

Credit points: 4

If desired, the lecture will be held in English.

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Prerequisites

Probability Calculus

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Intended Audience

Bachelor/Master students in Mathematics, Business Mathematics, Mathematical Biometrics and Finance, Diploma students in Mathematics, Business Mathematics

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Contents

This lecture broads and deepens methods and models discussed in Probability Calculus.

The main topics are:

• Markov chains in discrete time with finite state space
• Stationarity and ergodicity of Markov chains
• Markov-Chain-Monte-Carlo (MCMC)
• Reversibility and coupling algorithms

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Requirements and Exam

In order to become accredited for the written exam, one has to earn 50% of all homework credits.

Exam: Thursday, 29th July, 2pm - 4pm in H15

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Lecture notes

Lecture Notes (English version of 2010)

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Literature

This list of textbooks contains merely a small selection of books, which in addition to the lecture notes can be recommended for further reading.

• E. Behrends: Introduction to Markov Chains. Vieweg, 2000
• P. Bremaud: Markov Chains, Gibbs Fields, Monte Carlo Simulation, and Queues. Springer, 2008
• B. Chalmond: Modeling and Inverse Problems in Image Analysis. Springer, 2003
• D. Gamerman, H. Lopes: Markov Chain Monte Carlo: Stochastic Simulation for Bayesian Inference. Chapman & Hall, 2006
• O. Häggström: Finite Markov Chains and Algorithmic Applications. Cambridge University Press, 2002
• D.A. Levin, Y. Peres, E.L. Wilmer: Markov chains and mixing times. Publications of the AMS, 2009
• S. I. Resnick: Adventures in Stochastic Processes. Birkhäuser, 1992
• C. Robert, G. Casella: Introducing Monte Carlo Methods with R. Springer, 2009
• T. Rolski, H. Schmidli, V. Schmidt, J. Teugels: Stochastic Processes for Insurance and Finance. Wiley, 1999
• Y. Suhov, M. Kelbert: Probability and Statistics by Example. Volume 2. Markov Chains: A Primer in Random Processes and their Applications. Cambridge University Press, 2008
• H. Thorisson: Coupling, Stationarity, and Regeneration. Springer, 2002
• G. Winkler: Image Analysis, Random Fields and Dynamic Monte Carlo Methods. Springer, 2003