Markov Processes
Syllabus, Master's level, 1MS012
- 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)
- Finalised by
- The Faculty Board of Science and Technology, 15 March 2007
- Responsible department
- Department of Mathematics
Entry requirements
BSc, Inference Theory, or Probability and Statistics and Stochastic Modelling
Learning outcomes
In order to pass the course (grade 3) the student should be able to
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.
Reading list
- Reading list valid from Autumn 2023
- Reading list valid from Autumn 2022
- Reading list valid from Spring 2022
- Reading list valid from Spring 2019
- Reading list valid from Autumn 2015
- Reading list valid from Autumn 2013
- Reading list valid from Autumn 2009
- Reading list valid from Spring 2009, version 2
- Reading list valid from Spring 2009, version 1
- Reading list valid from Autumn 2008
- Reading list valid from Autumn 2007