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

None

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

See itslearning for syllabus lists and additional literature references.

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

56 hours per semester

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

Name E-mail Department
Kristian Debrabant debrabant@imada.sdu.dk Computational Science

Timetable

Administrative Unit

Institut for Matematik og Datalogi (matematik)

Team at Registration

NAT

Offered in

Odense

Recommended course of study

Profile Education Semester Offer period

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.