Advanced Probability Theory 1 (VidSand1)
Course content
- 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
Knowledge:
- 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
assignements.
Oral feedback during exercise classes, as a response to the
contribution of the students to the solution process of the
exercises.
- ECTS
- 7,5 ECTS
- Type of assessment
-
Written examination, 4 hours under invigilationSkriftlig prøve
- Aid
- All aids allowed
- 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)
- Category
- Hours
- Lectures
- 35
- Preparation
- 146
- Theory exercises
- 21
- Exam
- 4
- English
- 206
Kursusinformation
- Language
- English
- Course number
- NMAK11003U
- ECTS
- 7,5 ECTS
- Programme level
- Full Degree Master
- Duration
-
1 block
- Schedulegroup
-
A
- Capacity
- No limit
- Studyboard
- Study Board of Mathematics and Computer Science
Contracting department
- Department of Mathematical Sciences
Contracting faculty
- Faculty of Science
Course Coordinator
- Ernst Hansen (8-68756b6471766871437064776b316e7831676e)
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Courseinformation of students