# Syllabus for Markov Processes

Markovprocesser

A revised version of the syllabus is available.

## Syllabus

• 10 credits
• Course code: 1MS012
• Education cycle: Second cycle
• Main field(s) of study and in-depth level: Mathematics A1N
• Grading system: Fail (U), Pass (3), Pass with credit (4), Pass with distinction (5)
• Established: 2007-03-15
• Established by: The Faculty Board of Science and Technology
• Applies from: week 27, 2007
• Entry requirements: BSc, Inference Theory, or Probability and Statistics and Stochastic Modelling
• Responsible department: Department of Mathematics

## Learning outcomes

In order to pass the course (grade 3) the student should be able to

• give an account of important concepts and definitions in the area of the course;
• exemplify and interpret important concepts in specific cases;
• use the theory, methods and techniques of the course to solve mathematical statistical problems;
• express problems from relevant areas of applications in a form suitable for further mathematical statistical analysis, choose suitable models and solution techniques;
• interpret and asses results obtained;
• present mathematical statistical arguments to others.

Higher grades, 4 or 5, require a higher level of proficiency. The student should be able to treat and solve problems of greater complexity, i.e. problems requiring a combination of ideas and methods for their solution, and be able to give a more detailed account of the proofs of important theorems and by examples and counter-examples be able to motivate the scope of various results.
Requirements concerning the student's ability to present arguments and reasoning are greater.

## Content

The Markov property. The Chapman-Kolmogorov relation, classification of Markov processes, transition probability. Transition intensity, forward and backward equations. Stationary and asymptotic distribution. Convergence of Markov chains. Birth-death processes. Absorption probabilities, absorption time. Brownian motion and diffusion. Geometric Brownian motion. Generalised Markov models. Applications of Markov chains.

## Instruction

Lectures and problem solving sessions.

## Assessment

Written and, possibly, oral examination at the end of the course. Moreover, compulsory assignments may be given during the course.