2023 Autumn 2022 Autumn 2021 Autumn 2020 Autumn 2019 Autumn 2018 Autumn 2017 Autumn 2016 Autumn 2010 Autumn 2009 Autumn 2008 Autumn
Show the courses of study containg this course Se overgangsordninger
Dansk English

MM802: Stochastic Differential Equations I (10 ECTS)

STADS: 13002901

Level
Master's level course approved as PhD course

Teaching period
The course is offered in the autumn semester.

Teacher responsible
Email: debrabant@imada.sdu.dk

Timetable
Group Type Day Time Classroom Weeks Comment
Common I Monday 09-11 U23A 36,40
Common I Monday 10-12 U146 37
Common I Monday 09-11 U21 38
Common I Monday 09-11 U146 39
Common I Monday 09-11 U24A 41,43-46,51
Common I Wednesday 16-18 U23A 36,40
Common I Wednesday 16-18 U142 37-38
Common I Wednesday 16-18 U21 39
Common I Wednesday 16-18 U24A 41,43-45
Common I Friday 08-10 U143 36,40-41
Common I Friday 08-10 U146 37,39,44-45
Common I Friday 08-10 U21 38
Common I Friday 08-10 U141 43
Show entire timetable
 Show personal time table for this course.

Comment:
Ubegrænset deltagerantal.

Prerequisites:
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
Subject overview
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
    Meddeles ved kursets start.


Website
This course uses e-learn (blackboard).

Prerequisites for participating in the exam
None

Assessment and marking:
  1. Oral exam. Danish 7 mark scale, external examiner. (10 ECTS). (13002902).
Reexamination follows the rules of the study board.

Expected working hours
The teaching method is based on three phase model.
Intro phase: 28 hours
Skills training phase: 28 hours, hereof:
 - Tutorials: 28 hours

Educational activities

Educational form
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


Language
This course is taught in Danish or English, depending on the lecturer. However, if international students participate, the teaching language will always be English.

Course enrollment
See deadline of enrolment.

Tuition fees for single courses
See fees for single courses.