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
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Main field(s) of study and in-depth level:
Mathematics A1F,
Financial Mathematics A1F
- 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: 2013-04-23
- Revised by: The Faculty Board of Science and Technology
- Applies from: Autumn 2013
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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.
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
Compulsory assignments during the course.
Syllabus Revisions
- Latest syllabus (applies from Autumn 2020)
- Previous syllabus (applies from Spring 2019)
- Previous syllabus (applies from Autumn 2013)
- Previous syllabus (applies from Autumn 2012, version 2)
- Previous syllabus (applies from Autumn 2012, version 1)
- Previous syllabus (applies from Autumn 2009)
- Previous syllabus (applies from Autumn 2008, version 3)
- Previous syllabus (applies from Autumn 2008, version 2)
- Previous syllabus (applies from Autumn 2008, version 1)
- Previous syllabus (applies from Autumn 2007, version 2)
- Previous syllabus (applies from Autumn 2007, version 1)
Reading list
Reading list
Applies from: Autumn 2013
Some titles may be available electronically through the University library.
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Øksendal, Bernt
Stochastic differential equations : an introduction with applications
6. ed.: Berlin: Springer, 2003
Mandatory