Syllabus academic year 2011/2012
(Created 2011-09-01.)
MARKOV PROCESSESFMSF15
Credits: 7,5. Grading scale: TH. Cycle: G2 (First Cycle). Main field: Technology. Language of instruction: The course will be given in English on demand. FMSF15 overlaps following cours/es: FMS180 and MASC03. Optional for: C4, D4, D4ks, E4, E4pe, F4, F4bm, F4fm, F4ssr, Pi4, Pi4bm, Pi4fm, Pi4ssr. Course coordinator: Director of studies Anna Lindgren, studierektor@matstat.lu.se, Mathematical Statistics. Recommended prerequisits: A basic course in mathematical statistics. The course might be cancelled if the number of applicants is less than 16. Assessment: Written and oral 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: http://www.maths.lth.se/matstat/kurser/masc03/.

Aim
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

Contents
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.

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

Parts

Code: 0111. Name: Examination.
Higher education credits: 6,5. Grading scale: TH. Assessment: Written and oral examination.

Code: 0211. Name: Laboratory Work.
Higher education credits: 1. Grading scale: UG. Assessment: Laboratory work.