Advanced Probability Theory 1 (VidSand1)
- Sequences of random variables, almost sure convergence, Kolmogorov's 0-1 law.
- The strong law of large numbers.
- Weak convergence of probability measures. Characteristic functions.
- The central limit theorem. Triangular arrays and Lindebergs condition. The multivariate central limit theorem.
- The ergodic theorem.
MSc Programme in Actuarial Mathematics
MSc Programme in Mathematics
MSc Programme in Mathematics-Economics
MSc Programme in Statistics
- Fundamental convergence concepts and results in probability theory.
Skills: Ability to
- use the results obtained in the course to verify almost sure convergence or convergence in law of a sequence of random variables.
- verify conditions for the central limit theorem to hold.
- translate between sequences of random variables and iterative compositions of maps.
Competences: Ability to
- formulate and prove probabilistic results on limits of an infinite sequence of random variables.
- discuss the differences between the convergence concepts.
5 hours of lectures and 3 hours of exercises per week for 7 weeks.
Sandsynlighedsteori (Sand) - alternatively Mål- og integralteori
(MI) from previous years.
Academic qualifications equivalent to a BSc degree is recommended.
The course is similar to Stochastic Processes 2 (NMAB15025U).
It is not recommended to follow both courses.
Written feedback in the form of comments to the compulsory
Oral feedback during exercise classes, as a response to the
contribution of the students to the solution process of the
- 7,5 ECTS
- Type of assessment
Written examination, 4 hours under invigilationSkriftlig prøve
The course has been selected for ITX exam
- All aids allowed
The University will make computers available to students taking on-site exams at ITX. Students are therefore not permitted to bring their own computers, tablets or mobile phones. If textbooks and/or notes are permitted, according to the course description, these must be in paper format or uploaded through Digital Exam.
- Marking scale
- 7-point grading scale
- Censorship form
- External censorship
Criteria for exam assessment
The student must in a satisfactory way demonstrate that he/she has mastered the learning outcome of the course.
Single subject courses (day)
- Theory exercises
- Course number
- 7,5 ECTS
- Programme level
- Full Degree Master
- Block 1
- No limit
- Study Board of Mathematics and Computer Science
- Department of Mathematical Sciences
- Faculty of Science
- Ernst Hansen (8-67746a6370756770426f63766a306d7730666d)
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Courseinformation of students