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, 15 March 2007
- Responsible department
- Department of Mathematics
Entry requirements
BSc, Measure and Integration Theory I
Learning outcomes
In order to pass the course (grade 3) the student should be able to
Higher grades, 4 or 5, require a higher level of proficiency. The student should be able to solve problems of greater complexity, i.e. problems requiring a combination of ideas and methods for their solution, and be able to give a more detailed account of the proofs of important theorems and by examples and counter-examples be able to motivate the scope of various results. Requirements concerning the student's ability to present mathematical arguments and reasoning are greater.
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 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