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
  • Revised: 2008-11-03
  • Revised by: The Faculty Board of Science and Technology
  • Applies from: week 48, 2008
  • Entry requirements: 120 credits including 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

  • have a general knowledge of the theory of stochastic processes, in particular Markov processes, and be prepared to use Markov processes in various areas of applications;
  • be familiar with Markov chains in discrete and continuous time with respect to state diagram, recurrence and transience, classification of states, periodicity, irreducibility, etc., and be able to calculate transition probabilities and intensities;
  • be able to give an account of existence and uniqueness for stationary and asymptotic distributions of Markov chains and, whenever applicable, compute such distributions as solutions of a balance equation;
  • be able to calculate absorption probabilities and expected absorption time for Markov chains using the principle of conditioning with respect to the first jump;
  • be able to choose a suitable Markov model in various cases and make suitable calculations, in particular modelling of birth-death processes;
  • have a knowledge of Markov processes with a continuous state space, in particular a preparatory knowledge of Brownian motion and diffusion, and some understanding of the connection between the theory of Markov processes and differential equations;
  • have a knowledge of some general Markov method, e.g. Markov Chain Monte Carlo.

    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

    A revised version of the reading list is available.

    Applies from: week 04, 2009

    • Stirzaker, David Stochastic processes and models

      Oxford: Oxford Univ. Press, 2005

      Find in the library

    • Lawler, Gregory F. Introduction to stochastic processes

      2. ed.: 2006

      Find in the library

    • Norris, J. R. Markov chains

      1st pbk. ed.: New York: Cambridge University Press, 1998

      Find in the library

    Reading list revisions