# 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
• 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
• Applies from: week 27, 2007
• Entry requirements: BSc, Measure and Integration Theory I
• Responsible department: Department of Mathematics

## Learning outcomes

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

• give an account of important concepts and definitions in the area of the course;
• exemplify and interpret important concepts in specific cases;
• formulate important results and theorems covered by the course;
• describe the main features of the proofs of important theorems;
• express problems from relevant areas of applications in a mathematical form suitable for further analysis;
• use the theory, methods and techniques of the course to solve mathematical problems;
• present mathematical arguments to others.

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.