Kursernas Hemsidor

273023 Markovkedjor 5 sp - Markov Chains 5 cr

The course on Markov Chains treats the basics of Markov chains in discrete time: Chapman-Kolmogorov equations, transition probability matrices, classification of states, asymptotic behavior and stationary distributions, absorption problems and time reversibility, Markov Chain Monte Carlo methods, Hidden Markov Models (HMM), and other applications.

The course is lectured by PhD Daniel Aalto, e-mail address daaalto at åbo fi. The lectures are given in English. There will be theoretical and numerical exercises and assignments.

The course starts at 1 p.m. on Monday, 7 January 2013. Class hours are Mondays 13-15, Tuesdays 13-15 and Fridays 10-12. The venue is Hilbertrummet, ASA B329. Exercises are usually on Tuesdays. The course ends with a written examination on Friday 15 March at the last lecture (2 hours). The final exam can be substituted by a written assignment which is presented in the class. The topic for the assignment has to be chosen during January and the oral presentation given before the exam.

Literature: Sheldon M. Ross: Introduction to Probability Models 9th ed., Academic Press 2007; in particular Chapter 4. A small number of books are available at the student library in the ASA building. The lectures are strongly inspired by the book of D. A. Levin, Y. Peres, and E. L. Wilmer: "Markov Chains and Mixing times" available on http://pages.uoregon.edu/dlevin/MARKOV/markovmixing.pdf

Additional material may also be used. All material will be available in room B310.

Prerequisites: Analysis (Calculus), probability theory and a course on linear algebra or matrix calculus. Basic programming ability using a major mathematical programming package such as Mathematica, Matlab, or Maple is necessary.

Lectures and exercises. There will be no meeting on 8 Jan, 18 Feb, 19 Feb, and 22 Feb. Oral presentations can be given on 4 March and 8 March.

Monday 7 Jan: Introduction to the course, Definition of a Markov chain, Transition probability matrix, Frog and the two lily pads.

Tuesday 8 Jan: No meeting.

Friday 11 Jan: Random walk on a graph.

Monday 14 Jan:

Tuesday 15 Jan: First exercise session.

Senast uppdaterad: 2.1.2013