Syllabus for Measure Theory and Stochastic Integration

Måtteori och stokastisk integration

A revised version of the syllabus is available.

Syllabus

  • 5 credits
  • Course code: 1MA051
  • Education cycle: Second cycle
  • Main field(s) of study and in-depth level: Mathematics A1F, Financial Mathematics A1F

    Explanation of codes

    The code indicates the education cycle and in-depth level of the course in relation to other courses within the same main field of study according to the requirements for general degrees:

    First cycle

    • G1N: has only upper-secondary level entry requirements
    • G1F: has less than 60 credits in first-cycle course/s as entry requirements
    • G1E: contains specially designed degree project for Higher Education Diploma
    • G2F: has at least 60 credits in first-cycle course/s as entry requirements
    • G2E: has at least 60 credits in first-cycle course/s as entry requirements, contains degree project for Bachelor of Arts/Bachelor of Science
    • GXX: in-depth level of the course cannot be classified

    Second cycle

    • A1N: has only first-cycle course/s as entry requirements
    • A1F: has second-cycle course/s as entry requirements
    • A1E: contains degree project for Master of Arts/Master of Science (60 credits)
    • A2E: contains degree project for Master of Arts/Master of Science (120 credits)
    • AXX: in-depth level of the course cannot be classified

  • 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: 2009-08-27
  • Revised by: The Faculty Board of Science and Technology
  • Applies from: week 35, 2009
  • Entry requirements: 120 credit points including Measure and Integration Theory I
  • Responsible department: Department of Mathematics

Learning outcomes

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

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

    Content

    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.

    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 35, 2009

    Some titles may be available electronically through the University library.

    Reading list revisions