Measure Theory and Stochastic Integration
Syllabus, Master's level, 1MA051
- Code
- 1MA051
- Education cycle
- Second cycle
- Main field(s) of study and in-depth level
- Financial Mathematics A1F, Mathematics A1F
- Grading system
- Fail (U), Pass (3), Pass with credit (4), Pass with distinction (5)
- Finalised by
- The Faculty Board of Science and Technology, 24 October 2019
- Responsible department
- Department of Mathematics
Entry requirements
120 credits including Integration Theory, 10 credits. Integration Theory may be studied at the same time as 1MA051. Proficiency in English equivalent to the Swedish upper secondary course English 6.
Learning outcomes
On completion of the course, 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.
If there are special reasons for doing so, an examiner may make an exception from the method of assessment indicated and allow a student to be assessed by another method. An example of special reasons might be a certificate regarding special pedagogical support from the disability coordinator of the university.
Reading list
- Reading list valid from Spring 2021
- Reading list valid from Autumn 2020
- Reading list valid from Spring 2019, version 2
- Reading list valid from Spring 2019, version 1
- Reading list valid from Autumn 2013
- Reading list valid from Autumn 2012, version 2
- Reading list valid from Autumn 2012, version 1
- Reading list valid from Autumn 2010
- Reading list valid from Autumn 2009
- Reading list valid from Autumn 2008
- Reading list valid from Autumn 2007