NMAK24000U Stochastic Processes in Continuous Time

Volume 2024/2025

MSc Programme in Mathematics-Economics
MSc Programme in Mathematics
MSc Programme in Statistics
MSc Programme in Mathematics with a minor subject


This course examines mathematical concepts for stochastic calculus. The topics include

  • Introduction to continuous time stochastic processes
  • Definition and properties of Brownian motion
  • Semimartingales
  • Stochastic integration
  • Itô (change of variable) formula
  • Theorems for applications (e.g., Girsanov’s theorem)
Learning Outcome


  • Continuous time stochastic processes
  • Stochastic integrals
  • Itô formula and applications
  • continuous semimartingales
  • Stochastic differential equations


Skills: Ability to

  • Explain central concepts of continuous time of stochastic processes
  • Apply results from stochastic integration 
  • Apply Ito's formula
  • Apply theorems from stochastic calculus such as  Girsanov's theorem
  • Describe properties of stochastic differential equations


Compentencies: Ability to

  • Discuss and apply central methods and results from stochastic calculus 
  • Evaluate models based on stochastic integrals

See Absalon for a list of course literature.

Sandsynlighedsteori 2(Sand 2).
Academic qualifications equivalent to a BSc degree is recommended.
4 hours of lectures pr week for 7 weeks
2 hours of exercises pr week for 7 weeks
This course is equivalent to the first seven weeks of NMAK24001U Mathematical Finance
  • Category
  • Hours
  • Lectures
  • 28
  • Preparation
  • 163
  • Theory exercises
  • 14
  • Exam
  • 1
  • Total
  • 206
Continuous feedback during the course of the semester

Individual feedback can be received at the exercise classes upon active participation in exercise classes.

7,5 ECTS
Type of assessment
Oral examination, 30 minutes (no preparation)
Without aids
Marking scale
7-point grading scale
Censorship form
No external censorship
Exam period

Several internal examiners


Same as the ordinary exam

Criteria for exam assesment

The student should convincingly and accurately demonstrate the knowledge, skills and competences described under Intended learning outcome.