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