Syllabus academic year 2008/2009
(Created 2008-07-17.)

Higher education credits: 6. Grading scale: TH. Level: G2 (First level). Language of instruction: The course will be given in Swedish. FMS180 overlap following cours/es: MAS204, MAS204 och MASC03. Optional for: C3, D3, E3, E3pe, F3, F3sfm, I3, L4, L3XTG, M3, Pi3, Pi3bm, Pi3fm, Pi3sbs. Course coordinator: Director of studies Anna Lindgren,, Matematisk statistik. Recommended prerequisits: A basic course in mathematical statistics. Assessment: Written exam and compulsory computer exercises. Parts: 2. Further information: The course is also given at the faculty of science with the code MASC03. Home page:

Markov chains and processes are a class of models which, apart from a rich mathematical structure, also has applications in many disciplines, such as telecommunications and production (queue and inventory theory), reliability analysis, financial mathematics (e.g., hidden Markov models), automatic control, and image processing (Markov fields).

The aim of this course is to give the student the basic concepts and methods for Poisson processes, discrete Markov chains and processes, and also the ability to apply them. The course presents examples of applications in different fields, in order to facilitate the use of the knowledge in other courses where Markov models appear.

Knowledge and understanding
For a passing grade the student must

Skills and abilities
For a passing grade the student must

Judgement and approach
For a passing grade the student must

Markov chains: model graphs, Markov property, transition probabilities, persistent and transient states, positive and null persistent states, communication, existence and uniqueness of stationary distribution, and calculation thereof, absorption times.

Poisson process: Law of small numbers, counting processes, event distance, non-homogeneous processes, diluting and super positioning, processes on general spaces.

Markov processes: transition intensities, time dynamic, existence and uniqueness of stationary distribution, and calculation thereof, birth-death processes, absorption times.

Introduction to renewal theory and regenerative processes.

Lindgren, G. & Rydén, T.: Markovprocesser. KFS, 2002.


Code: 0109. Name: Examination.
Higher education credits: 5. Grading scale: TH. Assessment: Written exam.

Code: 0209. Name: Laboratory Work.
Higher education credits: 1. Grading scale: UG. Assessment: Computer exercises.