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: 25-04-2019


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 and the fundamentals of Hilbert space theory as well as stochastic variables, probability measures, convergence of stochastic variables, conditional expectations, and martingales.

Course introduction

The aim of the course is to give the students a thorough introduction to Ito integrals and their applications.

The
course builds on the knowledge acquired in the courses MM533
Mathematical and Numerical analysis, MM543 Measure and integration
theory and Banach spaces and MM544 Probability theory, and gives an
academic basis for a Master project in mathematics and for studying
advanced topics in Stochastic Differential Equations and Finance.

In relation to the competence profile of the degree it is the explicit focus of the course to:
  • Give skills to analyse, model and solve given problems at a high level of abstraction, based on logical and structured reasoning
  • Give skills to solve practical problems by using a combination of theory and numerical simulation
  • Give knowledge on advanced models and methods in mathematics

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

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

At the faculty of science, teaching is organized after the three-phase model ie. intro, training and study phase.
In order to enable students to achieve the learning objectives for the course, the teaching is organised in such a way that there are 56 lectures, class lessons, etc. on a semester.
These teaching activities are reflected in an estimated allocation of the workload of an average student as follows:

  • Intro phase (lectures, class lessons) - 28 hours
  • Training phase: 28 hours

Activities during the study phase:

  • 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 for all courses at the Faculty of Science are available at this link, unfortunately only in Danish.