Advanced topics in probability

The course can be part of the following programmes: 1) Mathematical Sciences, Master's Programme (N2MAT) and 2) Bachelor's Programme in Mathematics (N1MAT).

Main field of studies: Mathematical Statistics.

Specialization: A1F, Second cycle, has second-cycle course/s as entry requirements.

Department of Mathematical Sciences

Knowledge corresponding to the courses MSG110 Probability theory and MMA110 Integration theory.

The course provides an advanced treatment of selected topics in probability theory, with emphasis on limit theory and stochastic processes. Topics may include laws of large numbers, modes of convergence, random series, characteristic functions and central limit theorems, Brownian motion and other stochastic processes, geometric properties of random paths and sets, and connections between probability theory and analysis.

The selection and emphasis of topics may vary between course instances. Emphasis is placed on rigorous mathematical treatment of the selected topics, including fundamental results, proof techniques and applications.

On successful completion of the course the student will be able to:

• state and explain central concepts and results within the selected areas of advanced probability theory,
• formulate and prove selected fundamental results in probability theory using appropriate mathematical methods,
• apply advanced probabilistic methods and results to solve theoretical problems,
• analyse relationships between different probabilistic concepts and results and, where relevant, their connections to other areas of mathematics.

Lectures

Language of instruction: English

Oral exam.

If a student who has twice received a failing grade wishes to change examiner ahead of the next examination session, such a request should be made to the department in writing and should be approved by the department unless there are special reasons to the contrary (Chapter 6 Section 22 of the Higher Education Ordinance).

If a student has received a recommendation from the University of Gothenburg for study support for students with disabilities, the examiner may, where it is compatible with the learning outcomes of the course and provided that no unreasonable resources are required, decide to allow the student to sit an adjusted exam or alternative form of assessment.

In the event that a course has ceased or undergone major changes, students are to be guaranteed at least three examination sessions (including the ordinary examination session) over a period of at least one year, but no more than two years after the course has ceased/been changed. The same applies to internships and professional placements (VFU), although this is restricted to just one additional examination session.

The grading scale comprises Pass (G) and Fail (U).

The course will be evaluated at the end of the course together with the students. This will be followed by an anonymous survey.

The results of and possible changes to the course will be shared with students who participated in the evaluation and students who are starting the course.