
MM802: Stochastic Differential Equations I
The Study Board for Science
Teaching language: Danish or English depending on the teacher, but English if international students are enrolled
EKA: N310000102
Assessment: Second examiner: Internal
Grading: 7-point grading scale
Offered in: Odense
Offered in: Autumn
Level: Master's level course approved as PhD course
STADS ID (UVA): N310000101
ECTS value: 10
Date of Approval: 12-03-2025
Duration: 1 semester
Version: Approved - active
Comment
Entry requirements
Academic preconditions
Students taking the course are expected to have knowledge of measure and integration theory as well as stochastic variables, probability measures, convergence of stochastic variables, conditional expectations, and martingales as acquired in the courses MM533 Mathematical and Numerical analysis, MM543 Measure and integration theory and Banach spaces and MM544 Probability theory.
Course introduction
The aim of the course is to give the students a thorough introduction to Ito integrals and their applications.
Expected learning outcome
The learning objectives of the course are that the student demonstrates the ability to:
- Write down and solve stochastic differential equations on concrete situations within the contents of this course
- Give an oral presentation of the statement and proofs within the course syllabus
- Answer questions concerning definitions and results from the course syllabus
Content
The following main topics are contained in the course:
- Brownian motion
- Stochastic integration
- Itô’s formula
- Martingale representation theorem
- Existence and uniqueness of solutions to stochastic differential equations
- Time discrete approximation of stochastic differential equations
Literature
Examination regulations
Exam element a)
Timing
January
Tests
Oral exam
EKA
N310000102
Assessment
Second examiner: Internal
Grading
7-point grading scale
Identification
Student Identification Card - Name
Language
Normally, the same as teaching language
Examination aids
To be announced during the course
ECTS value
10
Additional information
Reexamination follows the rules of the study board.
Indicative number of lessons
Teaching Method
Planned lessons:
Total number of planned lessons: 56
Hereof:
Common lessons in classroom/auditorium: 56
The common classes use a modified version of the classic lecture, where the basic concepts and methods of the subject are presented, with both theory and examples. In these classes, there are opportunities for questions and discussion, and you will also work with exercises, which require thorough pre- and post-processing.
Other planned teaching activities:
- Preparation of exercises in study groups
- Contribution to online learning activities related to the course
- Immersion and preparation for the intro phase
Teacher responsible
Timetable
Administrative Unit
Team at Registration
Offered in
Recommended course of study
Transition rules
Transitional arrangements describe how a course replaces another course when changes are made to the course of study.
If a transitional arrangement has been made for a course, it will be stated in the list.
See transitional arrangements for all courses at the Faculty of Science.