NMAK24009U Topics in Probability

Volume 2026/2027
Education

MSc Programme in Mathematics

MSc Programme in Statistics

MSc Programme in Mathematics with a minor subject

MSc Programme in Mathematics-Economics

Content

We will cover various topics in probability theory, such as weak convergence theory, Gaussian processes, Levy processes, Feller processes, or concentration inequalities with the precise content varying each year, and depending on the interests of the participants.

Fall 2026: a tentative plan for this year is to give an introduction to the theory of Feller diffusions, a large and versatile class of continuouos-time Markov processes.  Emphasis will be on characterization via a second order differential operator known as the diffusion generator  and on applications of martingales constructed from this differential operator.  The relation to Ito-diffusions (solutions to certain stochastic differential equations) is examined, but no prior knowledge of stochastic differential equations is assummed.

 

Learning Outcome

Knowledge: To display knowledge of the course topics and content.

 

Skills: To be able to use the acquired knowledge to perform computations, and to read and understand current research papers.

 

Competencies: The student should be able to apply the theory to solve problems of moderate difficulty within the topics of the course

Knowledge of Markov processes and martingales in continuous time, corresponding to the course Brownian Motion

Academic qualifications equivalent to a BSc degree is recommended.
5 hours of lectures and 3 hours of exercise class for 7 weeks.
  • Category
  • Hours
  • Lectures
  • 35
  • Preparation
  • 149
  • Theory exercises
  • 21
  • Exam
  • 1
  • Total
  • 206
Written
Oral
Continuous feedback during the course of the semester

Written feedback in the form of comments to the compulsory assignements.

Oral feedback during exercise classes, as a response to the contribution of the students to the solution process of the exercises.

Credit
7,5 ECTS
Type of assessment
Oral examination, 30 minutes (30-minute preparation time)
Examination prerequisites

To participate in the exam the compulsory assignment must be approved and valid

Aid
All aids allowed

All aids allowed during preparation

Marking scale
7-point grading scale
Censorship form
No external censorship
Several internal examiners
Re-exam

Same as the ordinary exam.

If the compulsory assignment was not approved before the ordinary exam it must be (re)submitted and approved. It must be re(submitted) at the latest three weeks before the beginning of the re-exam week.

Criteria for exam assesment

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