Master’s studies

Syllabus for Measure Theory and Stochastic Integration

Måtteori och stokastisk integration


  • 5 credits
  • Course code: 1MA051
  • Education cycle: Second cycle
  • Main field(s) of study and in-depth level: Mathematics A1F, Financial Mathematics A1F
  • Grading system: Fail (U), 3, 4, 5.
  • Established: 2007-03-15
  • Established by: The Faculty Board of Science and Technology
  • Revised: 2013-04-23
  • Revised by: The Faculty Board of Science and Technology
  • Applies from: week 34, 2013
  • Entry requirements: 120 credits including Integration Theory, 10 credits, or Measure and Integration Theory I, 5 credits.
  • Responsible department: Department of Mathematics

Learning outcomes

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

  • interpret Brownian motion as a stochastic process on a filtered measurable space;
  • describe the class of continuous martingales;
  • describe the construction of a stochastic integral;
  • use Ito's formula;
  • describe the concept of "quadratic variation" and the martingale characterisation of Brownian motion;
  • formulate the representation theorem for martingales and how to use it;
  • formulate the existence and uniqueness theorems for stochastic differential equations;
  • use diffusion processes as a tool for mathematical modelling;
  • explain the connection between diffusion processes and solutions of parabolic and elliptic partial differential equations;
  • use Girsanov's representation theorem.


Brownian motion. Stochastic integration. Ito's formula. Continuous martingales. The representation theorem for martingales. Stochastic differential equations. Diffusion processes. Girsanov's representation theorem. Applications from selected areas.


Lectures and problem solving sessions.


Compulsory assignments during the course.

Reading list

Applies from: week 34, 2013

  • Øksendal, Bernt Stochastic differential equations : an introduction with applications

    6. ed.: Berlin: Springer, 2003

    Find in the library